2015
41
0
0
0
Upper and lower bounds for numerical radii of block shifts
2
2
For an nbyn 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.
1

15
27


P. Y.
Wu
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.
Department of Applied Mathematics, National
Taiwan, Province of China
pywu@math.nctu.edu.tw


H.L.
Gau
Department of Mathematics, National Central University, Chungli 32001, Taiwan.
Department of Mathematics, National Central
Taiwan, Province of China
hlgau@math.ncu.edu.tw
Numerical radius
block shift
minimum modulus
Higher numerical ranges of matrix polynomials
2
2
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.
1

29
45


Gh.
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Department of Pure Mathematics, Faculty of
Iran
aghamollaei@uk.ac.ir


M. A.
Nourollahi
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Department of Pure Mathematics, Faculty of
Iran
mnourollahi@bam.ac.ir
$k$Numerical range
matrix polynomial
companion linearization
basic $A$factor block circulant matrix
On nest modules of matrices over division rings
2
2
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 onesided 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 (onesided) ideals of nest algebras of matrices over division rings.
1

47
63


B. R.
Yahaghi
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 193955746, Iran.
Department of Mathematics, Faculty of Sciences,
Iran
bamdad5@hotmail.com


M.
RahimiAlangi
Department of Mathematics, Payame Noor University, P.O. Box 193953697 Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
mrahimi40@yahoo.com
Bimodule of rectangular matrices over a division ring
(left/right) submodule
subbimodule
(onesided) ideal
nest modules
Selfcommutators of composition operators with monomial symbols on the Bergman space
2
2
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 selfcommutator and antiselfcommutators of $C_varphi$. We also find the eigenfunctions of these operators.
1

65
76


A.
Abdollahi
Department of Mathematics, Shiraz University, Shiraz, Iran.
Department of Mathematics, Shiraz University,
Iran
abdollahi@shirazu.ac.ir


S.
Mehrangiz
Department of Engineering, Khonj Branch, Islamic Azad
University, Khonj, Iran.
Department of Engineering, Khonj Branch,
Iran
math.samira@yahoo.com


T.
Roientan
Department of Mathematics, Shiraz University, Shiraz, Iran.
Department of Mathematics, Shiraz University,
Iran
tahereh136355@yahoo.com
Bergman space
composition operator
essential spectrum
essential norm
selfcommutator
Linear maps preserving or strongly preserving majorization on matrices
2
2
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 $M_{nm}$.
1

77
83


F.
Khalooei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Department of Pure Mathematics, Faculty of
Iran
f_khalooei@uk.ac.ir
Linear preserver
row substochastic matrix
matrix majorization
Additive maps on C$^*$algebras commuting with $.^k$ on normal elements
2
2
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 conjugatelinear Jordan *homomorphism. If, moreover, the map $Phi$ commutes with $.^k$ on $mathcal{A}$, then $Phi$ is the sum of a linear *homomorphism and a conjugatelinear *homomorphism. In the case when $k not=1$, the assumption $Phi(I)$ being a projection can be deleted.
1

85
98


Y.
Guan
Department of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.
Department of Mathematics, Taiyuan University
China (P. R. C.)
yarongguan721@163.com


C.
Wang
Department of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.
Department of Mathematics, Taiyuan University
China (P. R. C.)
wangcailian1224@163.com


J.
Hou
Department of Mathematics, Taiyuan
University of Technology, Taiyuan 030024, P.R.
China.
Department of Mathematics, Taiyuan
University
China (P. R. C.)
jinchuanhou@aliyun.com
C$^*$algebras
additive maps
Jordan homomorphism
*homomorphism
A Haar wavelets approach to Stirling's formula
2
2
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.
1

99
106


M.
Ahmadinia
Department of Mathematics, University of Qom, P.O. Box 371853766, Qom, Iran.
Department of Mathematics, University of
Iran
mahdiahmadinia72@gmail.com


H.
Naderi Yeganeh
Department of Mathematics, University of Qom, P.O. Box 371853766, Qom, Iran.
Department of Mathematics, University of
Iran
hamid@hamidnaderiyeganeh.id.ir
Haar wavelets
Parseval's identity
Stirling's formula
Additivity of maps preserving Jordan $eta_{ast}$products on $C^{*}$algebras
2
2
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 nonzero complex number such that $etaneq1$, then $Phi$ is additive. Moreover, if $eta$ is rational<,> then $Phi$ is $ast$additive.
1

107
116


A.
Taghavi
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 474161468,
Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
taghavi@umz.ac.ir


H.
Rohi
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 474161468,
Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
h.rohi@stu.umz.ac.ir


V.
Darvish
Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 474161468,
Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
v.darvish@stu.umz.ac.ir
Maps preserving Jordan $eta*$product
Additive
Prime C*algebras
A note on lifting projections
2
2
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) 131149] that such a $p$ exists when $mathcal{A}$ has real rank zero.
1

117
122


D.
Hadwin
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
College of Engineering and Physical Sciences,
United States of America
don@unh.edu
C*algebra
projection
Toeplitz transforms of Fibonacci sequences
2
2
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.
1

123
132


L.
Connell
111 W. Westminster, Lake Forest, IL 60045.
111 W. Westminster, Lake Forest, IL 60045.
United States of America
lconnell@colby.edu


M.
Levine
The Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201.
The Catalyst Lofts, 141 41st Street, Pittsburgh,
United States of America
mjlevine@colby.edu


B.
Mathes
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
5839 Mayflower Hill, Colby College, Waterville,
United States of America
dbmathes@colby.edu


J.
Sukiennik
5839 Mayflower Hill, Colby College, Waterville, ME 04901.
5839 Mayflower Hill, Colby College, Waterville,
United States of America
justin.sukiennik@colby.edu
Hankel transform
Fibonacci numbers
Fibonacci identities
A note on approximation conditions, standard triangularizability and a power set topology
2
2
The main result of this article is that for collections of entrywise nonnegative 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, 298313], 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, 21912199] 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.
1

133
153


L.
Livshits
Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA.
Department of Mathematics and Statistics,
United States of America
llivshi@colby.edu
Simultaneous triangularizability
positive matrices
standard invariant subspaces
semigroups of operators
Addendum to: "Infinitedimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
2
2
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 ringtheoretic result to give a characterization of algebraically hyporeflexive transformations and the strict closure of the set of polynomials in a transformation $T$.
1

155
173


H.
Fan
University of New Hampshire
University of New Hampshire
United States of America
hun4@unh.edu


D.
Hadwin
College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.
College of Engineering and Physical Sciences,
United States of America
don@unh.edu
Abelian group
PID
Module
cyclic
torsion
locally algebraic
hyporeflexive
scalarreflexive ring
strict topology
Infinitedimensional versions of the primary, cyclic and Jordan decompositions
2
2
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.
1

175
183


M.
Radjabalipour
Erfan Institute of Higher Education, Kerman, Iran.
Erfan Institute of Higher Education, Kerman,
Iran
radjabalipour@ias.ac.ir
Jordan canonical form
rational canonical form
splitting field
Submajorization inequalities associated with $tau$measurable operators
2
2
The aim of this note is to study the submajorization inequalities for $tau$measurable operators in a semifinite von Neumann algebra on a Hilbert space with a normal faithful semifinite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..
1

185
194


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.
College of Mathematics and Statistics, Chongqing
China (P. R. C.)
jgzhao_dj@163.com


J.
Wu
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China.
College of Mathematics and Statistics, Chongqing
China (P. R. C.)
jlwu678@163.com
Submajorization
von Neumann algebra
$tau$measurable operators
The witness set of coexistence of quantum effects and its preservers
2
2
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), 227241.], we classify multiplicative general morphisms leaving the witness set invariant on finite dimensional Hilbert space effect algebras.
1

195
204


K.
He
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
College of Mathematics, Institute of Mathematics,
China (P. R. C.)
hk19830310@163.com


F. G.
Sun
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
College of Mathematics, Institute of Mathematics,
China (P. R. C.)
472974952@qq.com


J.
Hou
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
College of Mathematics, Institute of Mathematics,
China (P. R. C.)
65787687@qq.com


Q.
Yuan
College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.
College of Mathematics, Institute of Mathematics,
China (P. R. C.)
875675778@qq.com
Positive operator matrices
Coexistence
Hilbert space effect algebras
Isomorphisms