[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2008.45.2.313

SCHATTEN'S THEOREM ON ABSOLUTE SCHUR ALGEBRAS

Rakbud, Jitti (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE MAHIDOL UNIVERSITY)
Chaisuriya, Pachara (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE MAHIDOL UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 313-329 More about this Journal

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;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
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Reference

1	P. Chaisuriya and S.-C. Ong, Absolute Schur algebras and unbounded matrices, SIAM J. Matrix Anal. Appl. 20 (1999), no. 3, 596-605 DOI
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 DOI
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