Bounded linear operators on Banach function spaces of vector-valued functions

Gretsky, N. E.; Uhl, J. J.

doi:10.1090/S0002-9947-1972-0295110-3

Bounded linear operators on Banach function spaces of vector-valued functions
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by N. E. Gretsky and J. J. Uhl PDF

Trans. Amer. Math. Soc. 167 (1972), 263-277 Request permission

Abstract:

Representations of bounded linear operators on Banach function spaces of vector-valued functions to Banach spaces are given in terms of operator-valued measures. Then spaces whose duals are Banach function spaces are characterized. With this last information, reflexivity of this type of space is discussed. Finally, the structure of compact operators on these spaces is studied, and an observation is made on the approximation problem in this context.

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