Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Upper and lower bounds for numerical radii of block shifts 15 27 719 EN P. Y. Wu Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan. H.-L. Gau Department of Mathematics, National Central University, Chun-gli 32001, Taiwan. Journal Article 2014 09 04 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Higher numerical ranges of matrix polynomials 29 45 720 EN Gh. Aghamollaei Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. M. A. Nourollahi Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Journal Article 2014 10 15  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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 On nest modules of matrices over division rings 47 63 721 EN B. R. Yahaghi Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran. M. Rahimi-Alangi Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran. Journal Article 2014 09 15 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Self-commutators of composition operators with monomial symbols on the Bergman space 65 76 722 EN A. Abdollahi Department of Mathematics, Shiraz University, Shiraz, Iran. S. Mehrangiz Department of Engineering, Khonj Branch, Islamic Azad University, Khonj, Iran. T. Roientan Department of Mathematics, Shiraz University, Shiraz, Iran. Journal Article 2014 09 04 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Linear maps preserving or strongly preserving majorization on matrices 77 83 723 EN F. Khalooei Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Journal Article 2014 07 19 For $A,B\in M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $A\prec_{\ell}B$ (resp. $A\prec_{\ell s}B$), if $A=RB$ for some $n\times n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $\sim_{\ell s}$ on $M_{nm}$ as follows: $A\sim_{\ell s} B$ if $A\prec_{\ell s} B\prec_{\ell s} A.$ 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements 85 98 724 EN Y. Guan Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China. C. Wang Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China. J. Hou Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China. Journal Article 2014 09 08 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 $\Phi:\mathcal{A} \to\mathcal{B}$ is an additive map preserving $|\cdot|^k$ for all normal elements; that is, $\Phi(|A|^k)=|\Phi(A)|^k$ for all normal elements $A\in\mathcal A$, $\Phi(I)$ is a projection, and there exists a positive number $c$ such that $\Phi(iI)\Phi(iI)^{*}\leq c\Phi(I)\Phi(I)^{*}$, 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 A Haar wavelets approach to Stirling's formula 99 106 725 EN M. Ahmadinia Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran. H. Naderi Yeganeh Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran. Journal Article 2014 11 22 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras 107 116 726 EN A. Taghavi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran. H. Rohi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran. V. Darvish Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran. Journal Article 2014 11 26 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 $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ 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_46c90e129f3d8ce0cb2d465e7884246d.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 A note on lifting projections 117 122 727 EN D. Hadwin College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA. Journal Article 2015 04 11 Suppose $\pi:\mathcal{A}\rightarrow \mathcal{B}$ is a surjective unital $\ast$-homomorphism between C*-algebras $\mathcal{A}$ and $\mathcal{B}$, and $0\leq a\leq1$ with $a\in \mathcal{A}$. We give a sufficient condition that ensures there is a proection $p\in \mathcal{A}$ such that $\pi \left( p\right) =\pi \left( a\right)$. 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_582e0ada23e3758cdf98387770deec3b.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Toeplitz transforms of Fibonacci sequences 123 132 728 EN L. Connell 111 W. Westminster, Lake Forest, IL 60045. M. Levine The Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201. B. Mathes 5839 Mayflower Hill, Colby College, Waterville, ME 04901. J. Sukiennik 5839 Mayflower Hill, Colby College, Waterville, ME 04901. Journal Article 2015 04 28 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 A note on approximation conditions, standard triangularizability and a power set topology 133 153 729 EN L. Livshits Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA. Journal Article 2015 02 15 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_835c889d67bcda2cd2d6f303459aa8e6.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour 155 173 730 EN H. Fan University of New Hampshire D. Hadwin College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA. Journal Article 2015 05 23 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Infinite-dimensional versions of the primary, cyclic and Jordan decompositions 175 183 731 EN M. Radjabalipour Erfan Institute of Higher Education, Kerman, Iran. Journal Article 2015 02 07 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_9998ee94b22e27881824a5bc4920c986.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 Submajorization inequalities associated with $\tau$-measurable operators 185 194 732 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. J. Wu College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China. Journal Article 2014 11 02 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
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 41 Issue 7 (Special Issue) 2015 12 01 The witness set of coexistence of quantum effects and its preservers 195 204 733 EN K. He College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China. F. G. Sun College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China. J. Hou College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China. Q. Yuan College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China. Journal Article 2014 10 28 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