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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(l2) of bounded linear operators on l2 involving the duality relation among the class of compact operators K, the trace class C1 and B(l2). We also study the reflexivity in such the algebras.

SCHATTEN'S THEOREM ON ABSOLUTE SCHUR ALGEBRAS