A Generalization of Uniformly Rotund Banach Spaces
1979 ◽
Vol 31
(3)
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pp. 628-636
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Keyword(s):
Let X be a real Banach space. According to von Neumann's famous geometrical characterization X is a Hilbert space if and only if for all x, y ∈ XThus Hilbert space is distinguished among all real Banach spaces by a certain uniform behavior of the set of all two dimensional subspaces. A related characterization of real Lp spaces can be given in terms of uniform behavior of all two dimensional subspaces and a Boolean algebra of norm-1 projections [16]. For an arbitrary space X, one way of measuring the “uniformity” of the set of two dimensional subspaces is in terms of the real valued modulus of rotundity, i.e. for The space is said to be uniformly rotund if for each 0 we have .
2005 ◽
Vol 71
(1)
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pp. 107-111
Keyword(s):
1974 ◽
Vol 76
(1)
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pp. 157-159
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Keyword(s):
2002 ◽
Vol 133
(3)
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pp. 515-530
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1967 ◽
Vol 63
(3)
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pp. 613-629
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Keyword(s):
1973 ◽
Vol 9
(2)
◽
pp. 219-226
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1970 ◽
Vol 22
(5)
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pp. 994-996
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Keyword(s):
2010 ◽
Vol 10
(2)
◽
pp. 325-348
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2021 ◽
Vol 2021
◽
pp. 1-5