Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2008; 45(2): 313-329

Printed March 1, 2008

Copyright © The Korean Mathematical Society.

Schatten's theorem on absolute Schur algebras

Jitti Rakbud and Pachara Chaisuriya

Mahidol University, Mahidol University

Abstract

In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $\mathcal{B}(l_{2})$ of bounded linear operators on $l_{2}$ involving the duality relation among the class of compact operators $\mathcal{K}$, the trace class $\mathcal{C}_{1}$ and $\mathcal{B}(l_{2})$. We also study the reflexivity in such the algebras.

Keywords: Schur product, Banach algebra, dual space

MSC numbers: Primary 47L50; Secondary 47A10