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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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


Authors: N. E. Gretsky and J. J. Uhl
Journal: Trans. Amer. Math. Soc. 167 (1972), 263-277
MSC: Primary 47B99; Secondary 46E40
MathSciNet review: 0295110
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0295110-3
PII: S 0002-9947(1972)0295110-3
Keywords: Banach function spaces, vector-valued functions, representation of bounded linear operators, approximation property, Radon-Nikodym property
Article copyright: © Copyright 1972 American Mathematical Society