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Almost transitivity of some function spaces

Published online by Cambridge University Press:  24 October 2008

Peter Greim ,
James E. Jamison  and
Anna Kamińska
Peter Greim
Affiliation:
Department of Mathematics, The Citadel, Charleston, SC 29409, U.S.A.
James E. Jamison
Affiliation:
Department of Mathematics, The University of Memphis, Memphis, TN 38152, U.S.A.
Anna Kamińska
Affiliation:
Department of Mathematics, The University of Memphis, Memphis, TN 38152, U.S.A.
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Abstract

The almost transitive norm problem is studied for Lp (μ, X), C(K, X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp (μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the Lp-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp (μ, X) has almost transitive norm if Lp(μ) and X have. Separable spaces with non-trivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers and extreme points in the unit ball also fail to have almost transitive norms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 475 - 488
Copyright
Copyright © Cambridge Philosophical Society 1994

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