1992
DOI: 10.1007/bf02848940
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Property (β) implies normal structure of the dual space

Abstract: A.M.S. subject classification: 46B20.We prove that property (β) of Rolewicz implies normal structure of the dual space and we characterize spaces which are duals of spaces with property (β).

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Cited by 10 publications
(8 citation statements)
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“…Propositions 2.1 and 3.2 tell us that WUKK implies Bynum's condition. We note that this was also essentially shown in [14].…”
Section: Some Banach Space Propertiessupporting
confidence: 79%
See 1 more Smart Citation
“…Propositions 2.1 and 3.2 tell us that WUKK implies Bynum's condition. We note that this was also essentially shown in [14].…”
Section: Some Banach Space Propertiessupporting
confidence: 79%
“…Landes [14] defined WUKK , which results from replacing sep(x n ) > in the definition of WUKK by lim inf x n − x > . On the extraction of appropriate subsequences it can be seen that lim inf can be replaced by lim sup in the definition and WUKK can be written as: There exist an < 1 and a δ > 0 so that if x n ∈ B X and x n w − → x, then x ≤ 1 − δ if lim sup x n − x > .…”
Section: Some Banach Space Propertiesmentioning
confidence: 99%
“…In general, having property (β) is not a self-dual property of Banach spaces (see [21]). However, combining [21, Theorem 1] and Theorem 2 we have the following new result.…”
Section: Theoremmentioning
confidence: 99%
“…It was proved that if D(X) < 1, then X is reflexive and has normal structure [8]. Some classes of Banach spaces X for which D(X) < 1 were considered in [6].…”
Section: Introductionmentioning
confidence: 99%