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OPERATORS ON C0(L,X) WHOSE RANGE DOES NOT CONTAIN c0

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

Published online by Cambridge University Press:  01 June 2008

JARNO TALPONEN
JARNO TALPONEN*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Box 68, Gustaf Hällströminkatu 2b, FI-00014 Helsinki, Finland (email: talponen@cc.helsinki.fi)
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Abstract

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This paper contains two results: (a) if is a Banach space and (L,τ) is a nonempty locally compact Hausdorff space without isolated points, then each linear operator T:C0(L,X)→C0(L,X) whose range does not contain an isomorphic copy of c00 satisfies the Daugavet equality ; (b) if Γ is a nonempty set and X and Y are Banach spaces such that X is reflexive and Y does not contain c0 isomorphically, then any continuous linear operator T:c0(Γ,X)→Y is weakly compact.

Keywords

Daugavet equationweakly compact operatorsvector-valued function spaces

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 515 - 520
Copyright
Copyright © 2008 Australian Mathematical Society

References

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