Multiplication operators in Kothe-Bochner spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:373

Article

Calabuig, J. M.²  Rodriguez, J.¹  Sanchez-Perez, E. A.² 

[1] Univ Murcia, Fac Informat, Dept Matemat Aplicada, E-30100 Murcia, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

关键词: Multiplication operator;    Kothe-Bochner space;    Lebesgue-Bochner space;    Pettis integrable function;    Pettis norm;   

DOI  :  10.1016/j.jmaa.2010.07.038

来源: Elsevier

【 摘 要 】

Let X be a Banach space and E an order continuous Banach function space over a finite measure mu. We prove that an operator T in the Kothe-Bochner space E(X) is a multiplication operator (by a function in L(infinity)(mu)) if and only if the equality T(g < f, x*> x) = g < T(f), x*> x holds for every g is an element of L(infinity)(mu), f is an element of E(X), x is an element of X and x* is an element of X*. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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