p. 141 - 142 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |