A note on mutiplication operators on K the-Bochner spaces

作者：S S Khurana

来源：Acta Mathematica Universitatis Comenianae, 2012.

• Multiplication operator
• K the function spaces
• K the-Bochner function spaces.

Let (次, A, 米) is a finite measure space, E an order continuous Banach function space over 米, X a Banach space and E(X) the K the-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 Lㄓ) iff T(g f, x* %26gt; x) =g T(f), x* %26gt; x for every g Lㄓ, f E(X), x X, x* X*.

• 出版日期2012