Publication Type : Journal Article
Publisher : Rocky Mountain Mathematics Consortium
Source : Rocky Mountain Journal of Mathematics
Url : https://doi.org/10.1216/rmj.2021.51.1433
Campus : Haridwar
School : School of Engineering
Department : Mathematics
Year : 2021
Abstract : We discuss Arens regularity of the projective tensor product of Banach algebras consisting of Schatten class operators. More precisely, exploiting Ülger’s biregularity criterion, we prove that for any Hilbert space H , the Banach algebras S p ( H ) ⊗ γ S q ( H ) and B ( S 2 ( H ) ) ⊗ γ S 2 ( H ) are not Arens regular for every pair 1 ≤ p , q ≤ 2 ; whereas, when H is separable and S 2 ( H ) is equipped with the Schur product, we show that S 2 ( H ) is completely continuous and that S 2 ( H ) ⊗ γ S 2 ( H ) is Arens regular.
Cite this Research Publication : Lav Kumar Singh, On Arens regularity of projective tensor product of Schatten spaces, Rocky Mountain Journal of Mathematics, Rocky Mountain Mathematics Consortium, 2021, https://doi.org/10.1216/rmj.2021.51.1433