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On A Banach space property of Trubnikov

Published online by Cambridge University Press:  17 April 2009

Simeon Reich  and
Hong-Kun Xu
Simeon Reich
Affiliation:
Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel, e-mail: sreich@tx.technion.ac.il
Hong-Kun Xu
Affiliation:
Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa e-mail: hkxu@pixie.udw.ac.za
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Abstract

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Turbnikov/s property (U, λ, α, β) is investigated. In particular, it is shown that property (U, λ, α, α, − 1) with α > 1 is equivalent to α-uniform smoothness. It s also shown that property (U, 1, α, 1) with α > 1 is equivalent to the space being a Hilbert space. The dual property (U*, γ α α − 1) is also introduced and it is shown that a Banach space X has (U*, γ α, α − 1) if and only if X is α-uniformly convex.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 503 - 510
Copyright
Copyright © Australian Mathematical Society 2003

References

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