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Embedding ℓ1 into tensor products of Banach spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1470)

Abstract

It is known that if E and F are Banach spaces neither of which contains a copy of ℓ1, and if either E′ or F′ has the Radon-Nikodým property, then the ε-tensor product E

F does not contain a copy of ℓ1. We show that the converse of this assertion fails by showing that JH

JH fails to contain ℓ1.

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References

  1. J. Diestel, “Sequences and Series in Banach Spaces”, Graduate Texts in Mathematics, no.92, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1984.

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© 1991 Springer-Verlag

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Leung, D.H. (1991). Embedding ℓ1 into tensor products of Banach spaces. In: Odwell, E.E., Rosenthal, H.P. (eds) Functional Analysis. Lecture Notes in Mathematics, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090220

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  • DOI: https://doi.org/10.1007/BFb0090220

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54206-3

  • Online ISBN: 978-3-540-47493-7

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