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Real Banach Spaces with Numerical Index 1
Author(s) -
López Ginés,
Martín Miguel,
Payá Rafael
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939800513x
Subject(s) - mathematics , banach space , index (typography) , approximation property , mathematics subject classification , interpolation space , eberlein–šmulian theorem , reflexivity , property (philosophy) , banach manifold , pure mathematics , lp space , space (punctuation) , mathematical analysis , discrete mathematics , functional analysis , computer science , social science , biochemistry , chemistry , philosophy , epistemology , sociology , world wide web , gene , operating system
We show that an infinite‐dimensional real Banach space with numerical index 1 satisfying the Radon–Nikodym property contains l 1 . It follows that a reflexive or quasi‐reflexive real Banach space cannot be re‐normed to have numerical index 1, unless it is finite‐dimensional. 1991 Mathematics Subject Classification 46B20.