Weak sequential convergence in the dual of operator ideals

Abstract. By giving some necessary and sufficient conditions for the dual of operator subspaces to have the Schur property, we improve the results of Brown, Ülger and Saksman-Tylli in the Banach space setting. In particular, under some conditions on Banach spaces X and Y, we show that for a sub-spa...

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Bibliographic Details
Main Authors: S. M. Moshtaghioun, J. Zafarani
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Subjects:
Schur property
compact operator
operator ideal. MSC (2000
Primary 47L05
47L20
Secondary 46B28
46B99
tylli
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.561.6221
http://www.theta.ro/jot/archive/2003-049-001/2003-049-001-009.pdf
Description
Summary:Abstract. By giving some necessary and sufficient conditions for the dual of operator subspaces to have the Schur property, we improve the results of Brown, Ülger and Saksman-Tylli in the Banach space setting. In particular, under some conditions on Banach spaces X and Y, we show that for a sub-space M of operator ideal U(X,Y), M ∗ has the Schur property iff all point evaluations M1(x) = {Tx: T ∈ M1} and fM1(y∗) = {T ∗y ∗ : T ∈ M1} are relatively norm compact, where x ∈ X, y ∗ ∈ Y ∗ and M1 is the closed unit ball of M.

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