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On Banach spaces
having a Radon-Nikodým dual
C. Debiève |
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Vol. 120 (1985), No. 2, 327–330
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Abstract |
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The purpose of this paper is to prove a new characterisation of Banach spaces having a Radon-Nikodym dual, namely that if E is a Banach space, then E′ has the Radon-Nikodym property if and only if there exists an equivalent norm on E such that for each E-valued measure m of bounded variation, there exists an E′-valued function f with norm 1 |m|-a.e. such that |m| = f.m. |
Mathematical Subject Classification 2000
Primary: 46B22
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Milestones
Received: 10 March 1984
Published: 1 December 1985
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Authors |
| C. Debiève | |
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