weakly Chebyshev subspaces of banach spaces - Springer Link

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closed subspaces of a Banach space X are e-weakly Chebyshev if and only if X is ... Key Words e-quasi Chebyshev subspace, e-weakly Chebyshev subspace.
Analysis in Theory and Applications

19: 2, 2003, 130--135

E-WEAKLY SUBSPACES

CHEBYSHEV

OF BANACH

SPACES

Sh. Rezapour

(Azarbaidjan University of Tartn'at , Iran)

Received May 14, 2003

Abstract

We will define and characterize t-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are e-weakly Chebyshev if and only if X is reflexive. Key Words

e-quasi Chebyshev subspace, e-weakly Chebyshev subspace

AMS(2000)

subject classification

1

46B50, 41A65

Introduction and Preliminaries

Let X be a (complex or real) Banach space, e ~ 0 be given and let W be a subspace of X. A point y o E W is said to be an e-approximation (best approximation) for x E X if

IIx For x E X ,

-

yo

I1 ~
(b). SincePw,,(O)={gEW: Ilgll~ (a). It is obvious. Corollary 2.8.

(a) All closed subspaces of a Banach space X is e-weakly CHebyshev

in X i f and only i f X is reflexive. (b) Let W be a closed subspace of a Banach space X. Then, W is 3-weakly Chebyshev

in X for some ~ 0

i f and only i f W is e-weakly Chebyshev in X for all e>O.

Sh. Rezapour : t-Weakly Chebyshev Subspaces of Banach Spaces

135

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Tabriz, Iran

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