Extensions of certain operators to spaces of abstract integrable functions |
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| Authors: | N. Dinculeanu C. Ionescu Tulcea |
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| Affiliation: | 1. Mathematics Department, University of Florida, 32611, Gainesville, Florida, USA
2. Mathematics Department, Northwestern University, 60201, Evanston, Illinois, USA
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| Abstract: | In this paper we discuss the extension of operators onL 1 R spaces to operators onL 1 E andP 1 E spaces (see Section 1), whereE is a Banach space. A necessary and sufficient condition for the existence of the extension to a spaceP 1 E is given (see Section 3) whenE has the weak Radon-Nikodym property. The paper contains certain applications to ergodic theory and a theorem giving a characterization of weakly conditionally compact sets. |
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