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A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
Received: September 29, 2011; Accepted: January 10, 2012
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 every g Î L¥, f Î E(X), x Î X, x* Î X*.
Keywords: Multiplication operator; Köthe function spaces; Köthe-Bochner function spaces.
AMS Subject classification: Primary: 47B38, 46B42 Secondary: 28A25
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