On arens regularity of projective tensor product of Schatten p-class operators

Fuente: arXiv
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Autor principal: Singh, Lav Kumar
Formato: Preprint
Publicado: 2020
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author Singh, Lav Kumar
author_facet Singh, Lav Kumar
contents In this paper we discuss the Arens regularity of projective tensor product of Schatten p-class operators. We use the biregularity condition given by Ülger to prove that $S_p(\mathcal H)\otimes^γS_q(\mathcal H)$ is not Arens regular. We further prove that $B(S_2(\mathcal H))\otimes^γS_2(\mathcal H)$ is not Arens regular(with respect to usual multiplication) while it is regular with respect to Schur product. Thus we demonstrate the importance of biregularity condition given in \cite{Ulger} and the convenience of its use to prove Arens regularity or irregularity through some concrete examples.
format Preprint
id arxiv_https___arxiv_org_abs_2001_00830
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle On arens regularity of projective tensor product of Schatten p-class operators
Singh, Lav Kumar
Functional Analysis
Operator Algebras
47B10
In this paper we discuss the Arens regularity of projective tensor product of Schatten p-class operators. We use the biregularity condition given by Ülger to prove that $S_p(\mathcal H)\otimes^γS_q(\mathcal H)$ is not Arens regular. We further prove that $B(S_2(\mathcal H))\otimes^γS_2(\mathcal H)$ is not Arens regular(with respect to usual multiplication) while it is regular with respect to Schur product. Thus we demonstrate the importance of biregularity condition given in \cite{Ulger} and the convenience of its use to prove Arens regularity or irregularity through some concrete examples.
title On arens regularity of projective tensor product of Schatten p-class operators
topic Functional Analysis
Operator Algebras
47B10
url https://arxiv.org/abs/2001.00830