eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
15
27
719
Upper and lower bounds for numerical radii of block shifts
P. Y. Wu
pywu@math.nctu.edu.tw
1
H.-L. Gau
hlgau@math.ncu.edu.tw
2
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.
Department of Mathematics, National Central University, Chun-gli 32001, Taiwan.
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.
http://bims.iranjournals.ir/article_719_7b89cecc3c9d266bd2d8a5e08a8dc1cb.pdf
Numerical radius
block shift
minimum modulus
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
29
45
720
Higher numerical ranges of matrix polynomials
Gh. Aghamollaei
aghamollaei@uk.ac.ir
1
M. A. Nourollahi
mnourollahi@bam.ac.ir
2
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
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.
http://bims.iranjournals.ir/article_720_27058d5330da2190ea9a4d45104b7f64.pdf
$k$-Numerical range
matrix polynomial
companion linearization
basic $A$-factor block
circulant matrix
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
47
63
721
On nest modules of matrices over division rings
B. R. Yahaghi
bamdad5@hotmail.com
1
M. Rahimi-Alangi
mrahimi40@yahoo.com
2
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran.
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.
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.
http://bims.iranjournals.ir/article_721_5f9a18056601fd0fd44a34d75a22addd.pdf
Bimodule of rectangular matrices over a division ring
(left/right) submodule
subbimodule
(one-sided) ideal
nest modules
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
65
76
722
Self-commutators of composition operators with monomial symbols on the Bergman space
A. Abdollahi
abdollahi@shirazu.ac.ir
1
S. Mehrangiz
math.samira@yahoo.com
2
T. Roientan
tahereh136355@yahoo.com
3
Department of Mathematics, Shiraz University, Shiraz, Iran.
Department of Engineering, Khonj Branch, Islamic Azad University, Khonj, Iran.
Department of Mathematics, Shiraz University, Shiraz, Iran.
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.
http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf
Bergman space
composition operator
essential spectrum
essential norm
self-commutator
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
77
83
723
Linear maps preserving or strongly preserving majorization on matrices
F. Khalooei
f_khalooei@uk.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
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 $M_{nm}$.
http://bims.iranjournals.ir/article_723_2527aef09e5df50b63467d24125b54c8.pdf
Linear preserver
row substochastic matrix
matrix majorization
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
85
98
724
Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements
Y. Guan
yarongguan721@163.com
1
C. Wang
wangcailian1224@163.com
2
J. Hou
jinchuanhou@aliyun.com
3
Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China.
Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China.
Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China.
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.
http://bims.iranjournals.ir/article_724_15cc6b48cc93f3f328eb35b3ec30359a.pdf
C$^*$-algebras
additive maps
Jordan homomorphism
*-homomorphism
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
99
106
725
A Haar wavelets approach to Stirling's formula
M. Ahmadinia
mahdiahmadinia72@gmail.com
1
H. Naderi Yeganeh
hamid@hamidnaderiyeganeh.id.ir
2
Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.
Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.
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.
http://bims.iranjournals.ir/article_725_4334fc7b24c523ffe166068cee677ed5.pdf
Haar wavelets
Parseval's identity
Stirling's formula
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
107
116
726
Additivity of maps preserving Jordan $eta_{ast}$-products on $C^{*}$-algebras
A. Taghavi
taghavi@umz.ac.ir
1
H. Rohi
h.rohi@stu.umz.ac.ir
2
V. Darvish
v.darvish@stu.umz.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran.
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.
http://bims.iranjournals.ir/article_726_99688174344f34c677f1fe618917af2c.pdf
Maps preserving Jordan $eta*$-product
Additive
Prime C*-algebras
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
117
122
727
A note on lifting projections
D. Hadwin
don@unh.edu
1
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
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.
http://bims.iranjournals.ir/article_727_d877b46ffb88804bc8a9a508cad613ff.pdf
C*-algebra
projection
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
123
132
728
Toeplitz transforms of Fibonacci sequences
L. Connell
lconnell@colby.edu
1
M. Levine
mjlevine@colby.edu
2
B. Mathes
dbmathes@colby.edu
3
J. Sukiennik
justin.sukiennik@colby.edu
4
111 W. Westminster, Lake Forest, IL 60045.
The Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201.
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
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.
http://bims.iranjournals.ir/article_728_fac81767727c4a836e2fc2d91f8e8fed.pdf
Hankel transform
Fibonacci numbers
Fibonacci identities
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
133
153
729
A note on approximation conditions, standard triangularizability and a power set topology
L. Livshits
llivshi@colby.edu
1
Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA.
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.
http://bims.iranjournals.ir/article_729_43d144e4ed126793c4056a889f73dcfb.pdf
Simultaneous triangularizability
positive matrices
standard invariant subspaces
semigroups of operators
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
155
173
730
Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
H. Fan
hun4@unh.edu
1
D. Hadwin
don@unh.edu
2
University of New Hampshire
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
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 $T$.
http://bims.iranjournals.ir/article_730_312c207f682f4959e07b53c8cfb5db04.pdf
Abelian group
PID
Module
cyclic
torsion
locally algebraic
hyporeflexive
scalar-reflexive ring
strict topology
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
175
183
731
Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
M. Radjabalipour
radjabalipour@ias.ac.ir
1
Erfan Institute of Higher Education, Kerman, Iran.
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.
http://bims.iranjournals.ir/article_731_8937987b904454c3bdd4f748e6f5d775.pdf
Jordan canonical form
rational canonical form
splitting field
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
185
194
732
Submajorization inequalities associated with $tau$-measurable operators
J. Zhao
jgzhao_dj@163.com
1
J. Wu
jlwu678@163.com
2
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China, and College of Science, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China.
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..
http://bims.iranjournals.ir/article_732_bff972f6998e185187ad5bd0a9ee72b7.pdf
Submajorization
von Neumann algebra
$tau$-measurable operators
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2015-12-01
41
Issue 7 (Special Issue)
195
204
733
The witness set of coexistence of quantum effects and its preservers
K. He
hk19830310@163.com
1
F. G. Sun
472974952@qq.com
2
J. Hou
65787687@qq.com
3
Q. Yuan
875675778@qq.com
4
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China.
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China.
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China.
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China.
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.
http://bims.iranjournals.ir/article_733_11e420ffa346edde192a2c50f80bc9b4.pdf
Positive operator matrices
Coexistence
Hilbert space effect algebras
Isomorphisms