Bounded Linear Operators on Banach Function Spaces of Vector-Valued Functions
Open Access
- 1 May 1972
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 167, 263-277
- https://doi.org/10.2307/1996138
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.Keywords
This publication has 11 references indexed in Scilit:
- Projecting the space of bonded operators onto the space of compact operatorsProceedings of the American Mathematical Society, 1970
- Linear operations tensor products, and contractive projections in function spacesStudia Mathematica, 1970
- Martingale Convergence and the Radon-Nikodym Theorem in Banach Spaces.MATHEMATICA SCANDINAVICA, 1968
- Representation theorems on Banach function spacesMemoirs of the American Mathematical Society, 1968
- Some Examples of Normed Köthe SpacesPublished by Springer Nature ,1966
- Functional Analysis and Semi-groups. (Revised Edition) By Einai Hille and Ralph S. Phillips. Pp. xii, 808. $13.80, 1957. Americaj Mathematical Society Colloquium Publications, Vol 31. (American Mathematical Society)The Mathematical Gazette, 1959
- Some Remarks on Banach Function SpacesIndagationes Mathematicae, 1956
- A general bilinear vector integralStudia Mathematica, 1955
- On Weakly Compact Subsets of a Banach SpaceAmerican Journal of Mathematics, 1943
- Linear Operations on Summable FunctionsTransactions of the American Mathematical Society, 1940