منابع مشابه
Fractal Functions and Schauder Bases
1. Introduction. In recent years more and more attention has been paid in mathematical papers to fractal functions and to fractal sets. There are various definitions of those objects. We assume that a compact set K ∈ R d+1 is fractal, by definition, if its box (entropy) dimension dim b (K) = j for j = 0, 1,. .. , d + 1 and 0 < dim b (K) < d + 1. At the same time the function f : I d → R d , I =...
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Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. Mathematics Subject Classification (2000). 46B03.
متن کاملA Characterization of Schauder Frames Which Are Near-schauder Bases
A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we study this problem using the notion of a minimal-associated sequence space and a minimal-associated reconstruction operator for Schauder frames. We prove that a Schauder frame is a near...
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We construct a computable Banach space which possesses a Schauder basis, but does not possess any computable Schauder basis.
متن کاملOn Equivalence Relations Generated by Schauder Bases
Let (xn) be a sequence in a Banach space X. We denote coef(X, (xn)) = {a ∈ R : ∑ n a(n)xn converges}. In this talk, we focus on Borel reducibility between equivalence relations of RN/coef(X, (xn)). This kind of research begin from Dougherty and Hjorth’s results on R/`p (p ≥ 1) and R/c0. School of Mathematical Sciences, Nankai University, Tianjin, 300071, P.R.China E-mail address: dinglongyun@gm...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1970
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-22-1-91-110