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

1993
*
Journal of combinatorial theory. Series A
*

A lower bound is found for

doi:10.1016/0097-3165(93)90056-e
fatcat:7l44b26qv5dktbmjas7urnupsa
*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. ...##
###
Spectra and pseudospectra of block Toeplitz matrices

1998
*
Linear Algebra and its Applications
*

This paper extends previous work by Reichel and Trefethen

doi:10.1016/s0024-3795(97)00311-x
fatcat:bhm2drznmjfhdbjdkwhkixesuu
*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. ...##
###
Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators

2018
*
Malaysian Journal of Fundamental and Applied Sciences
*

We provide

doi:10.11113/mjfas.v14n4.881
fatcat:rx6u7mzqnbafzbfayhznupfmte
*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. ...##
###
Discrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators

2010
*
Automatika
*

In

doi:10.1080/00051144.2010.11828388
fatcat:5izfr6avyzegfadxxchlmatb6y
*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 + ...##
###
Positive definite matrices with Hermitian blocks and their partial traces
[article]

2012
*
arXiv
*
pre-print

A few corollaries are given, in particular

arXiv:1208.6494v3
fatcat:dglrpbhfuvenpb6pop6aml3cfq
*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 ...##
###
Almost commuting matrices

1979
*
Journal of Functional Analysis
*

T be

doi:10.1016/0022-1236(79)90071-5
fatcat:576lg6wvcfhm5l3w5glsngd45m
*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. ...##
###
Joint spectral radius and Hölder regularity of wavelets

2000
*
Computers and Mathematics with Applications
*

Then, we generate

doi:10.1016/s0898-1221(00)00148-6
fatcat:fpjfw2bowvcappyh5dxesqebbe
*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. ...##
###
On the complete boundedness of the Schur block product
[article]

2018
*
arXiv
*
pre-print

We give a Stinespring representation

arXiv:1712.05285v3
fatcat:jayyxo4njngl5fvcxmnawnjgv4
*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*. ...##
###
On the complete boundedness of the Schur block product

2018
*
Proceedings of the American Mathematical Society
*

We give a Stinespring representation

doi:10.1090/proc/14202
fatcat:a7hohmyjqbajpkooelnh3cazcy
*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*. ...##
###
Asymptotics of eigenvalues of infinite block matrices

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. ...

##
###
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]

2019
*
arXiv
*
pre-print

Given two m x n

arXiv:1811.03668v3
fatcat:d6k7ecw5obbqtklz4hvhlfrvgi
*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] . ...##
###
Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
[article]

2018
*
arXiv
*
pre-print

We provide

arXiv:1801.08158v2
fatcat:4legguey2nesbmhtcxpenner4i
*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). ...
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