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An estimate on the norm of the product of infinite block operator matrices

John Lindsay Orr
1993 Journal of combinatorial theory. Series A  
A lower bound is found for the operator norm of the product of two infinite block operator matrices on Hilbert space which depends only on the norms of submatrices of these operators.  ...  The methodology of the paper is to study sequence-valued functions on certain families of finite sets (the barriers of Nash-Williams) and show that the convex hulls of the ranges of any pair of such functions  ...  INTRODUCTION Let (Xi.j) and (Y+,/) be two infinite block operator matrices acting on the same countably infinite direct sum of Hilbert spaces.  ... 
doi:10.1016/0097-3165(93)90056-e fatcat:7l44b26qv5dktbmjas7urnupsa

Spectra and pseudospectra of block Toeplitz matrices

Andrew Lumsdaine, Deyun Wu
1998 Linear Algebra and its Applications  
This paper extends previous work by Reichel and Trefethen on the spectra and pseudospectra of Toeplitz matrices to the case of triangular block Toeplitz matrices.  ...  In particular, we give results for the pseudospectra of triangular block Toeplitz matrices and operators and show that the pseudospectrum of a triangular block Toeplitz matrix converges to the pseudospectrum  ...  The authors also thank the referee for several kind suggestions to improve this paper.  ... 
doi:10.1016/s0024-3795(97)00311-x fatcat:bhm2drznmjfhdbjdkwhkixesuu

Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators

Arnon Ploymukda, Pattrawut Chansangiam
2018 Malaysian Journal of Fundamental and Applied Sciences  
We provide estimations for the operator norm, the trace norm, and the Hilbert-Schmidt norm for Khatri-Rao products of Hilbert space operators.  ...  It follows that the Khatri-Rao product is continuous on norm ideals of compact operators equipped with the topologies induced by such norms.  ...  The notion of Kronecker product of matrices is extended to the tensor product of operators on a Hilbert space.  ... 
doi:10.11113/mjfas.v14n4.881 fatcat:rx6u7mzqnbafzbfayhznupfmte

Discrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators

Przemysław Orłowski
2010 Automatika  
In the paper a method for norm estimation of transfer operator defined on infinite time horizon is proposed.  ...  An operational equivalent of the transfer function for linear timevarying systems is transfer operator.  ...  in one of the two equivalent notations: either an evolutionary one, where operators are written by means of sums and products [3] : y (k) = ĈN x 0 (k) + ĈLBv (k) + D (k) v (k) = C (k) ϕ k−1 k 0 x 0 +  ... 
doi:10.1080/00051144.2010.11828388 fatcat:5izfr6avyzegfadxxchlmatb6y

Positive definite matrices with Hermitian blocks and their partial traces [article]

Jean-Christophe Bourin, Eun-Young Lee, Minghua Lin
2012 arXiv   pre-print
A few corollaries are given, in particular the partial trace operation increases norms of separable states on a real Hilbert space, leading to a conjecture for usual complex Hilbert spaces.  ...  Then, for all symmetric norms, equation* H <∑_s=1^β A_s,s. equation* The proof uses a nice decomposition for positive matrices and unitary congruences with the generators of a Clifford algebra.  ...  We will prove a norm inequality and give some applications, a rearrangement inequality and an estimate for operators acting on tensor product spaces that are of interest in the setting of quantum theory  ... 
arXiv:1208.6494v3 fatcat:dglrpbhfuvenpb6pop6aml3cfq

Almost commuting matrices

Carl Pearcy, Allen Shields
1979 Journal of Functional Analysis  
T be an operator on s?.  ...  If the answer to this question is affirmative, then one could pass to the limit and have an analogous result for compact operators on infinite-dimensional Hilbert space.  ... 
doi:10.1016/0022-1236(79)90071-5 fatcat:576lg6wvcfhm5l3w5glsngd45m

Joint spectral radius and Hölder regularity of wavelets

M. Maesumi
2000 Computers and Mathematics with Applications  
Then, we generate an optimal unit ball by taking the convex hull of the action of the semigroup of matrices, scaled by their joint radius, on the invariant ball of the scaled optimal product.  ...  Wavelets of compact support can be generated via infinite products of certain matrices. The rate of growth of these products determines the regularity of the wavelet.  ...  The solution of this equation can be determined from infinite products of certain fixed matrices whose entries depend on the coefficient of the dilation equation.  ... 
doi:10.1016/s0898-1221(00)00148-6 fatcat:fpjfw2bowvcappyh5dxesqebbe

On the complete boundedness of the Schur block product [article]

Erik Christensen
2018 arXiv   pre-print
We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_ij), B:=  ...  This implies an inequality due to Livshits and two apparently new ones on diagonals of matrices.  ...  The basic tool we used in that study is a result on the operator norm of the Schur product between a pair of operator valued matrices.  ... 
arXiv:1712.05285v3 fatcat:jayyxo4njngl5fvcxmnawnjgv4

On the complete boundedness of the Schur block product

Erik Christensen
2018 Proceedings of the American Mathematical Society  
We give a Stinespring representation of the Schur block product on pairs of square matrices with entries in a C *algebra as a completely bounded bilinear operator of the form: such that V is an isometry  ...  This implies an inequality due to Livshits and 2 more ones, apparently new, on the diagonals of matrices: operator, row and column norm;  ...  The basic tool we used in that study is a result on the operator norm of the Schur product between a pair of operator valued matrices.  ... 
doi:10.1090/proc/14202 fatcat:a7hohmyjqbajpkooelnh3cazcy

Asymptotics of eigenvalues of infinite block matrices

I N Braeutigam, Dmitry Mikhailovich Polyakov
2019 Ufimskii Matematicheskii Zhurnal  
The paper is devoted to determining the asymptotic behavior of eigenvalues, which is one of topical directions in studying operators generated by tridiagonal infinite block matrices in Hilbert spaces of  ...  Namely, we provide asymptotics for the eigenvalues of symmetric and non-symmetric tridiagonal infinite matrices in the scalar case, the asymptotics for arithmetical means of the eigenvalues of block matrices  ...  In the following examples we consider infinite block tridiagonal matrices. 3.  ... 
doi:10.13108/2019-11-3-11 fatcat:yzj2laxykjccna7jhw45ajc37m

Page 5563 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
This problem for blocks of operators on an infinite-dimensional Hilbert space is studied as well, together with applications to spectral completion and assignment (the infinite- dimensional analogues of  ...  Uniform operator-norm bounds for the perturbation of the Moore-Penrose inverse of such an operator are given assuming that the closure of the range of the perturbed operator intersects the orthogonal complement  ... 

Page 5511 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
°, converges to an operator which is paracontracting with respect to this norm. We deduce the conti- nuity of the limit of the product of matrices as a function of the sequences {i, }?°).  ...  Summary: “We develop conditions under which a product []?<, 7; of matrices chosen from a possibly infinite set of matrices Y = {T;: 7 € J} converges.  ... 

Page 701 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
Suffi- cient conditions on these products are provided that imply submul- tiplicativity with respect to the spectral norm and certain of the unitarily invariant norms.  ...  (IL-TLAV; Tel Aviv) Similarity of block diagonal and block triangular matrices. (English summary) Integral Equations Operator Theory 15 (1992), no. 5, 853-863.  ... 

Decompositions of Schur block products [article]

Erik Christensen
2019 arXiv   pre-print
Given two m x n matrices A = (a_ij) and B=(b_ij) with entries in B(H), the Schur block product is the m x n matrix A B := (a_ijb_ij).  ...  There exists an m x n contraction matrix S = (s_ij), such that A B = diag(AA*)^(1/2) S diag(B*B)^(1/2). This decomposition is also valid for the block Schur tensor product.  ...  INTRODUCTION A substantial part of this note is a direct consequence of our previous work on the block Schur product of matrices with operator entries presented in [3] .  ... 
arXiv:1811.03668v3 fatcat:d6k7ecw5obbqtklz4hvhlfrvgi

Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox [article]

Dario A. Bini, Stefano Massei, Leonardo Robol
2018 arXiv   pre-print
We provide an algorithmic description of these operations on the finite parametrization of QT-matrices, and we develop a MATLAB toolbox implementing them in a transparent way.  ...  The toolbox is then extended to perform arithmetic operations on matrices of finite size that have a Toeplitz plus low-rank structure.  ...  In particular, one can show that T (a) 2 a W , where T (a) 2 denotes the operator norm induced by the ℓ 2 -norm on the operator T (a).  ... 
arXiv:1801.08158v2 fatcat:4legguey2nesbmhtcxpenner4i
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