Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Upper and lower bounds for numerical radii of block shifts
15
27
EN
P. Y.
Wu
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.
pywu@math.nctu.edu.tw
H.-L.
Gau
Department of Mathematics, National Central University, Chun-gli 32001, Taiwan.
hlgau@math.ncu.edu.tw
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine when either of them becomes an equality.
Numerical radius,block shift,minimum modulus
http://bims.iranjournals.ir/article_719.html
http://bims.iranjournals.ir/article_719_7b89cecc3c9d266bd2d8a5e08a8dc1cb.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Higher numerical ranges of matrix polynomials
29
45
EN
Gh.
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
aghamollaei@uk.ac.ir
M. A.
Nourollahi
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
mnourollahi@bam.ac.ir
Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical range of the basic $A$-factor block circulant matrix, which is the block companion matrix of the matrix polynomial $P(lambda) = lambda ^m I_n - A$, is studied.
$k$-Numerical range,matrix polynomial,companion linearization,basic $A$-factor block
circulant matrix
http://bims.iranjournals.ir/article_720.html
http://bims.iranjournals.ir/article_720_27058d5330da2190ea9a4d45104b7f64.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
On nest modules of matrices over division rings
47
63
EN
B. R.
Yahaghi
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran.
bamdad5@hotmail.com
M.
Rahimi-Alangi
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.
mrahimi40@yahoo.com
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We then characterize submodules of nest modules of matrices over $D$ in terms of certain finite sequences of left row reduced echelon or right column reduced echelon matrices with entries from $D$. We use this result to characterize principal submodules of nest modules. We also describe subbimodules of nest modules of matrices. As a consequence, we characterize (one-sided) ideals of nest algebras of matrices over division rings.
Bimodule of rectangular matrices over a division ring,(left/right) submodule,subbimodule,(one-sided) ideal,nest modules
http://bims.iranjournals.ir/article_721.html
http://bims.iranjournals.ir/article_721_5f9a18056601fd0fd44a34d75a22addd.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Self-commutators of composition operators with monomial symbols on the Bergman space
65
76
EN
A.
Abdollahi
Department of Mathematics, Shiraz University, Shiraz, Iran.
abdollahi@shirazu.ac.ir
S.
Mehrangiz
Department of Engineering, Khonj Branch, Islamic Azad
University, Khonj, Iran.
math.samira@yahoo.com
T.
Roientan
Department of Mathematics, Shiraz University, Shiraz, Iran.
tahereh136355@yahoo.com
Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_varphi$. We also find the eigenfunctions of these operators.
Bergman space,composition operator,essential spectrum,essential norm,self-commutator
http://bims.iranjournals.ir/article_722.html
http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Linear maps preserving or strongly preserving majorization on matrices
77
83
EN
F.
Khalooei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
f_khalooei@uk.ac.ir
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear preservers and all linear strong preservers of $prec_{ell s}$ and $sim_{ell s}$ from $M_{nm}$ to $M_{nm}$.
Linear preserver,row substochastic matrix,matrix majorization
http://bims.iranjournals.ir/article_723.html
http://bims.iranjournals.ir/article_723_2527aef09e5df50b63467d24125b54c8.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements
85
98
EN
Y.
Guan
Department of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.
yarongguan721@163.com
C.
Wang
Department of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.
wangcailian1224@163.com
J.
Hou
Department of Mathematics, Taiyuan
University of Technology, Taiyuan 030024, P.R.
China.
jinchuanhou@aliyun.com
Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a positive number $c$ such that $Phi(iI)Phi(iI)^{*}leq
cPhi(I)Phi(I)^{*}$, then $Phi$ is the sum of a linear Jordan *-homomorphism and a conjugate-linear Jordan *-homomorphism. If, moreover, the map $Phi$ commutes with $|.|^k$ on $mathcal{A}$, then $Phi$ is the sum of a linear *-homomorphism and a conjugate-linear *-homomorphism. In the case when $k not=1$, the assumption $Phi(I)$ being a projection can be deleted.
C$^*$-algebras,additive maps,Jordan homomorphism,*-homomorphism
http://bims.iranjournals.ir/article_724.html
http://bims.iranjournals.ir/article_724_15cc6b48cc93f3f328eb35b3ec30359a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
A Haar wavelets approach to Stirling's formula
99
106
EN
M.
Ahmadinia
Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.
mahdiahmadinia72@gmail.com
H.
Naderi Yeganeh
Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.
hamid@hamidnaderiyeganeh.id.ir
This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.
Haar wavelets,Parseval's identity,Stirling's formula
http://bims.iranjournals.ir/article_725.html
http://bims.iranjournals.ir/article_725_4334fc7b24c523ffe166068cee677ed5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Additivity of maps preserving Jordan $eta_{ast}$-products on $C^{*}$-algebras
107
116
EN
A.
Taghavi
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.
taghavi@umz.ac.ir
H.
Rohi
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.
h.rohi@stu.umz.ac.ir
V.
Darvish
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.
v.darvish@stu.umz.ac.ir
Let $mathcal{A}$ and $mathcal{B}$ be two $C^{*}$-algebras such that $mathcal{B}$ is prime. In this paper, we investigate the additivity of maps $Phi$ from $mathcal{A}$ onto $mathcal{B}$ that are bijective, unital and satisfy $Phi(AP+eta PA^{*})=Phi(A)Phi(P)+eta Phi(P)Phi(A)^{*},$ for all $Ainmathcal{A}$ and $Pin{P_{1},I_{mathcal{A}}-P_{1}}$ where $P_{1}$ is a nontrivial projection in $mathcal{A}$. If $eta$ is a non-zero complex number such that $|eta|neq1$, then $Phi$ is additive. Moreover, if $eta$ is rational then $Phi$ is $ast$-additive.
Maps preserving Jordan $eta*$-product,Additive,Prime C*-algebras
http://bims.iranjournals.ir/article_726.html
http://bims.iranjournals.ir/article_726_99688174344f34c677f1fe618917af2c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
A note on lifting projections
117
122
EN
D.
Hadwin
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
don@unh.edu
Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real rank zero, textit{J. Funct. Anal.} {99} (1991) 131--149] that such a $p$ exists when $mathcal{A}$ has real rank zero.
C*-algebra,projection
http://bims.iranjournals.ir/article_727.html
http://bims.iranjournals.ir/article_727_d877b46ffb88804bc8a9a508cad613ff.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Toeplitz transforms of Fibonacci sequences
123
132
EN
L.
Connell
111 W. Westminster, Lake Forest, IL 60045.
lconnell@colby.edu
M.
Levine
The Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201.
mjlevine@colby.edu
B.
Mathes
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
dbmathes@colby.edu
J.
Sukiennik
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
justin.sukiennik@colby.edu
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
Hankel transform,Fibonacci numbers,Fibonacci identities
http://bims.iranjournals.ir/article_728.html
http://bims.iranjournals.ir/article_728_fac81767727c4a836e2fc2d91f8e8fed.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
A note on approximation conditions, standard triangularizability and a power set topology
133
153
EN
L.
Livshits
Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA.
llivshi@colby.edu
The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2, 298--313], and [A. A. Jafarian, H. Radjavi, P. Rosenthal and A. R. Sourour, Simultaneous, triangularizability, near commutativity and Rota's theorem, Trans. Amer. Math. Soc. 347, (1995), no. 6, 2191--2199] on the approximations and triangularizability of collections of operators and matrices. In conclusion we introduce and explore a related topology on the power sets of metric spaces.
Simultaneous triangularizability,positive matrices,standard invariant subspaces,semigroups of operators
http://bims.iranjournals.ir/article_729.html
http://bims.iranjournals.ir/article_729_43d144e4ed126793c4056a889f73dcfb.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
155
173
EN
H.
Fan
University of New Hampshire
hun4@unh.edu
D.
Hadwin
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
don@unh.edu
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminology of linear transformations. We add an additional translation of a ring-theoretic result to give a characterization of algebraically hyporeflexive transformations and the strict closure of the set of polynomials in a transformation $T$.
Abelian group,PID,Module,cyclic,torsion,locally algebraic,hyporeflexive,scalar-reflexive ring,strict topology
http://bims.iranjournals.ir/article_730.html
http://bims.iranjournals.ir/article_730_312c207f682f4959e07b53c8cfb5db04.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
175
183
EN
M.
Radjabalipour
Erfan Institute of Higher Education, Kerman, Iran.
radjabalipour@ias.ac.ir
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
Jordan canonical form,rational canonical form,splitting field
http://bims.iranjournals.ir/article_731.html
http://bims.iranjournals.ir/article_731_8937987b904454c3bdd4f748e6f5d775.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
Submajorization inequalities associated with $tau$-measurable operators
185
194
EN
J.
Zhao
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China, and
College of Science, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China.
jgzhao_dj@163.com
J.
Wu
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China.
jlwu678@163.com
The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..
Submajorization,von Neumann algebra,$\tau$-measurable operators
http://bims.iranjournals.ir/article_732.html
http://bims.iranjournals.ir/article_732_bff972f6998e185187ad5bd0a9ee72b7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
41
Issue 7 (Special Issue)
2015
12
01
The witness set of coexistence of quantum effects and its preservers
195
204
EN
K.
He
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
hk19830310@163.com
F. G.
Sun
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
472974952@qq.com
J.
Hou
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
65787687@qq.com
Q.
Yuan
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
875675778@qq.com
One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness set invariant. Furthermore, applying linear maps preserving commutativity, which are characterized by Choi, Jafarian and Radjavi [Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227--241.], we classify multiplicative general morphisms leaving the witness set invariant on finite dimensional Hilbert space effect algebras.
Positive operator matrices,Coexistence,Hilbert space effect algebras,Isomorphisms
http://bims.iranjournals.ir/article_733.html
http://bims.iranjournals.ir/article_733_11e420ffa346edde192a2c50f80bc9b4.pdf