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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)
  • Published : 2008.03.31

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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  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 https://doi.org/10.1007/BF01203176
  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