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ON λ-STRICT IDEALS IN BANACH SPACES

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  27 September 2010

TROND A. ABRAHAMSEN  and
OLAV NYGAARD
TROND A. ABRAHAMSEN*
Affiliation:
Department of Mathematics, University of Agder, Postbox 422, 4604 Kristiansand, Norway (email: [email protected])
OLAV NYGAARD
Affiliation:
Department of Mathematics, University of Agder, Postbox 422, 4604 Kristiansand, Norway (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We define and study λ-strict ideals in Banach spaces, which for λ=1 means strict ideals. Strict u-ideals in their biduals are known to have the unique ideal property; we prove that so also do λ-strict u-ideals in their biduals, at least for λ>1/2. An open question, posed by Godefroy et al. [‘Unconditional ideals in Banach spaces’, Studia Math.104 (1993), 13–59] is whether the Banach space X is a u-ideal in Ba(X), the Baire-one functions in X**, exactly when κu(X)=1; we prove that if κu(X)=1 then X is a strict u-ideal in Ba (X) , and we establish the converse in the separable case.

Keywords

strict idealu-idealVN-subspace

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 231 - 240
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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