J. Korean Math. Soc. 2008; 45(2): 313-329
Printed March 1, 2008
Copyright © The Korean Mathematical Society.
Jitti Rakbud and Pachara Chaisuriya
Mahidol University, Mahidol University
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
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