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A note on mutiplication operators on Köthe-Bochner spaces

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Author(s): S. S. Khurana

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXI;
Issue: 1;
Start page: 141;
Date: 2012;
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Keywords: Multiplication operator | K&#246 | the function spaces | K&#246 | the-Bochner function spaces

ABSTRACT
Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g < f, x* > x) =g < T(f), x* > x for everyg Î L¥, f Î E(X), x Î X, x* Î X*.
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