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SCHATTEN`S THEOREM ON ABSOLUTE SCHUR ALGEBRAS
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 Title & Authors
SCHATTEN`S THEOREM ON ABSOLUTE SCHUR ALGEBRAS
Rakbud, Jitti; Chaisuriya, Pachara;
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 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 of bounded linear operators on involving the duality relation among the class of compact operators K, the trace class and . We also study the reflexivity in such the algebras.
 Keywords
Schur product;Banach algebra;dual space;
 Language
English
 Cited by
 References
1.
P. Chaisuriya and S.-C. Ong, Absolute Schur algebras and unbounded matrices, SIAM J. Matrix Anal. Appl. 20 (1999), no. 3, 596-605 crossref(new window)

2.
N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7 Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958

3.
L. Livshits, S.-C. Ong, and S.-W. Wang, Banach space duality of absolute Schur algebras, Integral Equations Operator Theory 41 (2001), no. 3, 343-359 crossref(new window)

4.
R. E. Megginson, An Introduction to Banach Space Theory, Graduate Texts in Mathematics, 183. Springer-Verlag, New York, 1998

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