منابع مشابه
Schauder bases under uniform renormings
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 کاملFractal 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 =...
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...
متن کاملOn the Effective Existence of Schauder Bases
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: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.2307/2036579