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The Radon-Nikodým Property for the Space of Operators, I

✍ Scribed by J. Diestel; T. J. Morrison

Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
343 KB
Volume
92
Category
Article
ISSN
0025-584X

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✦ Synopsis

Some necessary and some sufficient conditions for the space of all bounded linear operators between two BANACH spaces to have the RADON-NIKODPM property are given.

In recent years the study of BANACH spaces for which the RADON-NIKODPM theorem is valid has been enthusiastically joined by a number of mathematicians. This interest is due on the one hand to the striking geometric properties enjoyed by spaces with the RADON-NIKODPM property and on the other hand to the deep operator-theoretic consequences of RADON-NIKODPM theory in BANACH spaces. In some sense the most rewarding aspect of this recent progress is that i t is not usually difficult to establish that a given space has the RADON-NIKODPM property, (see the results below) yet once established so much follows; it is almost as though one is getting something for nothing.

The reader interested in an extensive discussion of the RADON-NIKODPM theorem for measures with values in BANACH spaces is referred to DIESTEL-UHL [1976a]. More recent results are discussed in DIESTEL-UHL [1976b]. Math. 17, 113-115 (1972).

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