Title : ( Chebyshev Centers and Approximation in Pre-Hilbert C* -Modules )
Authors: Asadollah Niknam , - - ,
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Abstract
We extend the study of Chebyshev centers in pre-Hilbert C-modules by considering the C-algebra valued map defined by |x| = hx, xi1/2. We prove that if T is a remotal subset of a pre- Hilbert C-module M, and F M is star-shaped at a relative Chebyshev center c of T with respect to F, then |x − qT (x)|2 |x−c|2 +|c−qT (c)|2(x 2 F). The uniqueness of Chebyshev center follows from this inequality. This is a generalization of a well-known result on Hilbert spaces.
Keywords
, C*-algebra, Inner Derivation, Infinitsimal generator
@article{paperid:1019944,
author = {Niknam, Asadollah and -, -},
title = {Chebyshev Centers and Approximation in Pre-Hilbert C* -Modules},
journal = {Bulletin of the Iranian Mathematical Society},
year = {2010},
volume = {36},
number = {2},
month = {November},
issn = {1735-8515},
pages = {209--216},
numpages = {7},
keywords = {C*-algebra; Inner Derivation; Infinitsimal generator},
}
%0 Journal Article
%T Chebyshev Centers and Approximation in Pre-Hilbert C* -Modules
%A Niknam, Asadollah
%A -, -
%J Bulletin of the Iranian Mathematical Society
%@ 1735-8515
%D 2010
