论文标题
关于Schatten P级操作员的投射张量产品的定期性
On arens regularity of projective tensor product of Schatten p-class operators
论文作者
论文摘要
在本文中，我们讨论了Schatten P级运营商投射张量产品的定期性。我们使用ülger给出的双重条件证明$ s_p（\ mathcal h）\ otimes^γs_q（\ mathcal h）$不是普通的。我们进一步证明$ b（s_2（\ mathcal h））\ otimes^γs_2（\ mathcal h）$不是Arens常规（相对于通常的乘法），而对于Schur产品是规则的。因此，我们证明了在\ cite {ulger}中给出的双重条件的重要性，以及通过某些具体示例证明其规律性或不规则性的便利性。
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.
