# SCHATTEN'S THEOREM ON ABSOLUTE SCHUR ALGEBRAS

• Rakbud, Jitti ;
• Chaisuriya, Pachara
• Published : 2008.03.31
• 101 10

#### 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 $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

#### Keywords

Schur product;Banach algebra;dual space

#### References

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5. J. Rakbud and P. Chaisuriya, Classes of infinite matrices over Banach algebras, J. Anal. Appl. 3 (2005), no. 1, 31-46