Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Upper and lower bounds for numerical radii of block shifts1527719ENP. Y.WuDepartment of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.H.-L.GauDepartment of Mathematics, National Central University, Chun-gli 32001, Taiwan.Journal Article20140904For 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Higher numerical ranges of matrix polynomials2945720ENGh.AghamollaeiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.M. A.NourollahiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20141015 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201On nest modules of matrices over division rings4763721ENB. R.YahaghiDepartment of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran.M.Rahimi-AlangiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.Journal Article20140915Let $ 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Self-commutators of composition operators with monomial symbols on the Bergman space6576722ENA.AbdollahiDepartment of Mathematics, Shiraz University, Shiraz, Iran.S.MehrangizDepartment of Engineering, Khonj Branch, Islamic Azad
University, Khonj, Iran.T.RoientanDepartment of Mathematics, Shiraz University, Shiraz, Iran.Journal Article20140904Let $\varphi(z)=z^m, z \in \mathbb{U}$, 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Linear maps preserving or strongly preserving majorization on matrices7783723ENF.KhalooeiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20140719For $A,B\in M_{nm},$ 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements8598724ENY.GuanDepartment of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.C.WangDepartment of Mathematics, Taiyuan University of Technology, Taiyuan
030024, P.R. China.J.HouDepartment of Mathematics, Taiyuan
University of Technology, Taiyuan 030024, P.R.
China.Journal Article20140908Let $\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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201A Haar wavelets approach to Stirling's formula99106725ENM.AhmadiniaDepartment of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.H.Naderi YeganehDepartment of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.Journal Article20141122This 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras107116726ENA.TaghaviDepartment of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.H.RohiDepartment of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.V.DarvishDepartment of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, P.O. Box 47416-1468,
Babolsar, Iran.Journal Article20141126Let $\mathcal{A}$ 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201A note on lifting projections117122727END.HadwinCollege of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.Journal Article20150411Suppose $\pi:\mathcal{A}\rightarrow \mathcal{B}$ 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Toeplitz transforms of Fibonacci sequences123132728ENL.Connell111 W. Westminster, Lake Forest, IL 60045.M.LevineThe Catalyst Lofts, 141 41st Street, Pittsburgh, PA 15201.B.Mathes5839 Mayflower Hill, Colby College, Waterville, ME 04901.J.Sukiennik5839 Mayflower Hill, Colby College, Waterville, ME 04901.Journal Article20150428We 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201A note on approximation conditions, standard triangularizability and a power set topology133153729ENL.LivshitsDepartment of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA.Journal Article20150215The 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour155173730ENH.FanUniversity of New HampshireD.HadwinCollege of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.Journal Article20150523In 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Infinite-dimensional versions of the primary, cyclic and Jordan decompositions175183731ENM.RadjabalipourErfan Institute of Higher Education, Kerman, Iran.Journal Article20150207The 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Submajorization inequalities associated with $\tau$-measurable operators185194732ENJ.ZhaoCollege of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China, and
College of Science, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China.J.WuCollege of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China.Journal Article20141102The 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.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201The witness set of coexistence of quantum effects and its preservers195204733ENK.HeCollege of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.F. G.SunCollege of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.J.HouCollege of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.Q.YuanCollege of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi,
030024, P.R. China.Journal Article20141028One 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