On arens regularity of projective tensor product of Schatten p-class operators
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866911819596038144 |
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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 |