Onc 0 sequences in Banach spaces
Copyright policy )Onc 0 sequences in Banach spaces
A Banach space has property (S) if every normalized weakly null sequence contains a subsequence equivalent to the canonical basis of \((c_ 0)\). It is shown that equivalence constants can be choosen independent of the original sequence. It is also shown that property (S) implies property (a) introduced by \textit{A. Pelczynski} [Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron Phys. 6, 251-253 (1958; Zbl 0082.108)]. This settles - in the negative - a conjecture by \textit{J. Hagler} [Stud. Math. 60, 289-307 (1977; Zbl 0387.46015)] that certain separable Banach spaces with property (a) have separable duals.
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Isomorphic theory (including renorming) of Banach spaces, Duality and reflexivity in normed linear and Banach spaces, property (a), Classical Banach spaces in the general theory, property (S)
Isomorphic theory (including renorming) of Banach spaces, Duality and reflexivity in normed linear and Banach spaces, property (a), Classical Banach spaces in the general theory, property (S)
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