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arXiv · 2001.00830

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

Lav Kumar Singh
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Abstract

In this paper we discuss the Arens regularity of projective tensor product of Schatten p-class operators. We use the biregularity condition given by \"Ulger to prove that $S_p(\mathcal H)\otimes^\gamma S_q(\mathcal H)$ is not Arens regular. We further prove that $B(S_2(\mathcal H))\otimes^\gamma S_2(\mathcal H)$ 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.

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Lav Kumar Singh. 2020-01-02. On arens regularity of projective tensor product of Schatten p-class operators. https://doi.org/10.1216/rmj.2021.51.1433

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