Renorming in the space of Bochner integrable functionsL
1(μ,X) |
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Authors: | G Schlüchtermann |
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Institution: | 1. Mathematisches Institut der Universit?t München, Theresienstrasse 39, W-8000, München 2, Germany
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Abstract: | A sufficient condition is given when a subspaceL⊂L
1(μ,X) of the space of Bochner integrable function, defined on a finite and positive measure space (S, Φ, μ) with values in a Banach spaceX, is locally uniformly convex renormable in terms of the integrable evaluations {∫
A
fdμ;f∈L}. This shows the lifting property thatL
1(μ,X) is renormable if and only ifX is, and indicates a large class of renormable subspaces even ifX does not admit and equivalent locally uniformly convex norm. |
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Keywords: | |
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