Vol. 87, No. 1, 1980

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Neighborly bushes and the Radon-Nikodým property for Banach spaces

Philip W. McCartney

Vol. 87 (1980), No. 1, 157–168
Abstract

We introduce the neighborly bush property (NBP). A dual Banach space has the NBP if and only if it contains a bush, but there is a Banach space with the NBP that does not contain a bush and therefore has the Radon-Nikodým property. Any Banach space with the NBP has a nonseparable second dual. Other related results are obtained.

Mathematical Subject Classification 2000
Primary: 46B22
Milestones
Received: 18 October 1978
Revised: 5 June 1979
Published: 1 March 1980
Authors
Philip W. McCartney