Illinois Journal of Mathematics

Types of Radon-Nikodym properties for the projective tensor product of Banach spaces

Qingying Bu, Joe Diestel, Patrick Dowling, and Eve Oja

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Abstract

Let $X$ and $Y$ be Banach spaces such that $X$ has a boundedly complete basis. Then $X\hat{\otimes}Y$, the projective tensor product of $X$ and $Y$, has the Radon-Nikodym property (resp.~the analytic Radon-Nikodym property, the near Radon-Nikodym property, contains no copy of $c_0$) if and only if $Y$ has the same property.

Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1303-1326.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138106

Digital Object Identifier
doi:10.1215/ijm/1258138106

Mathematical Reviews number (MathSciNet)
MR2037005

Zentralblatt MATH identifier
1039.46053

Subjects
Primary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10]
Secondary: 46E40: Spaces of vector- and operator-valued functions 46M05: Tensor products [See also 46A32, 46B28, 47A80]

Citation

Bu, Qingying; Diestel, Joe; Dowling, Patrick; Oja, Eve. Types of Radon-Nikodym properties for the projective tensor product of Banach spaces. Illinois J. Math. 47 (2003), no. 4, 1303--1326. doi:10.1215/ijm/1258138106. https://projecteuclid.org/euclid.ijm/1258138106


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