HEREDITARY PROPERTIES OF CERTAIN IDEALS OF COMPACT OPERATORS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 41, Issue 3, 2004, pp.457-464
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2004.41.3.457

Title & Authors

HEREDITARY PROPERTIES OF CERTAIN IDEALS OF COMPACT OPERATORS

Cho, Chong-Man; Lee, Eun-Joo;

Cho, Chong-Man; Lee, Eun-Joo;

Abstract

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either or has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).

Keywords

ideal;M-ideal;H B-subspace;property SU;compact operator;

Language

English

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