Abstract
Generalizations of the Banach-Saks property were used by several authors to characterize reflexive Banach spaces (cf. [11], [12], and [16]). We give a characterization of separable conjugate Banach spaces by a similar summability condition. As a consequence, we obtain analogous characterizations of separable second conjugate Banach spaces and of quasi-reflexive spaces. Nonseparable conjugate Banach spaces possessing a smooth predual are also characterized in terms of a summability condition.
The results of this paper are part of the author's doctoral dissertation written under the supervision of Professor D. Kölzow at the University of Erlangen, Germany, in 1981. More details will be published elsewhere.
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© 1983 Springer-Verlag
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Brigola, R. (1983). On summability in conjugate Banach spaces. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061555
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DOI: https://doi.org/10.1007/BFb0061555
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