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- W2401228465 abstract "Abstract. In this paper, we show that Schlumprecht space is re-flexive and the Dual of Schlumprecht space has the Banach-Saksproperty and study behavior of block basic sequence in Schlumprec-ht space. 1. IntroductionS. Banach and S. Saks [BS] showed that every bounded sequence inL p [0,1], 1 < p < ∞, has a subsequence with arithmetic means con-verging in norm. J. Schrier [Sc] showed that C[0,1] does not have thisproperty. The above results lead us to consider the following ques-tion. What Banach space X has the Banach-Saks property i.e., everybounded sequence in X admits a subsequence whose arithmetic meansconverges in norm. S. Kakutani [Ka] showed that uniformly convexBanach spaces have the Banach-Saks property. T. Nishiura and D.Waterman [NW] showed that Banach spaces with the Banach-Saksproperty are reflexive. A. Baernstein [Ba] proved the converse by pro-viding an example of a reflexive Banach space which does not havethe Banach-Saks property. C. Seifert [Se1] showed that the dual ofBaernstein space has the Banach-Saks property. In this paper, we in-troduce arbitrarily distortable Banach space - Schlumprecht space [Sh]and show that it is reflexive, not uniformly convex and its dual has theBanach-Saks property.Schlumprecht [Sh] introduced a Banach space which is arbitrar-ily distortable. We introduce some basic definitions and constructSchlumprecht space S. The vector space of all real valued sequences" @default.
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- W2401228465 date "1998-01-01" @default.
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- W2401228465 title "BANACH-SAKS PROPERTY ON THE DUAL OF SCHLUMPRECHT SPACE" @default.
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