Biconcave-function characterisations of UMD and Hilbert spaces
1993 ◽
Vol 47
(2)
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pp. 297-306
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Keyword(s):
Suppose that X is a real or complex Banach space with norm |·|. Then X is a Hilbert space if and only iffor all x in X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and |x − Y| ≤ 2 almost everywhere. This leads to the following biconcave-function characterisation: A Banach space X is a Hilbert space if and only if there is a biconcave function η: {(x, y) ∈ X × X: |x − y| ≤ 2} → R such that η(0, 0) = 2 andIf the condition η(0, 0) = 2 is eliminated, then the existence of such a function η characterises the class UMD (Banach spaces with the unconditionally property for martingale differences).
Keyword(s):
2005 ◽
Vol 71
(1)
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pp. 107-111
Keyword(s):
2007 ◽
Vol 2007
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pp. 1-7
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1978 ◽
Vol 21
(2)
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pp. 213-219
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Keyword(s):
1977 ◽
Vol 24
(2)
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pp. 129-138
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1985 ◽
Vol 97
(2)
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pp. 321-324
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1980 ◽
Vol 87
(1)
◽
pp. 47-50
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1997 ◽
Vol 56
(2)
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pp. 303-318
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Keyword(s):