Entropy of subshifts and Macaev norm
type: Item
instance of: scholarly article
title: Entropy of subshifts and Macaev norm
zbMATH Open document ID: 1062.47030
author: Rui Okayasu
published in: Journal of the Mathematical Society of Japan
publication date: 2004-08-16T00:00:00Z
review text: Let \(H\) be a separable infinite-dimensional Hilbert space and \(\Sigma^0_\Phi\) be a symmetrically normed ideal with a symmetric norming function \(\Phi\). If \(\tau= (T_1,\dots, T_N)\) is an \(N\)-tuple of bounded linear operators, then the number \(k_\Phi(\tau)\) is defined by \(\liminf_{u\in{\mathbf F}({\mathbf H})^+_1}\,\max_{1\leq a\leq N}\,\| [u, T_a]\|\), where the inferior limit is taken with respect to the natural order on \({\mathbf F}({\mathbf H})^+_1\) and \([A, B]= AB- BA\). In the present paper, the exact value of Voiculescu's invariant \(k^-_\infty(\tau)\) is obtained, see \textit{D. Voiculescu} [J. Funct. Anal. 91, No. 1, 1--36 (1990; Zbl 0762.46051)].
reviewed by: Dumitrŭ Popa
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 2092013
zbMATH Keywords: Hilbert space
zbMATH Keywords: symmetrically normed ideal
zbMATH Keywords: Macaev ideal
zbMATH Keywords: Fock space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191418701
OpenAlex ID: W2136633421
DOI: 10.2969/JMSJ/1191418701
description: scientific article; zbMATH DE number 2092013