CHEBYSHEV CENTERS AND APPROXIMATION IN PRE-HILBERT C*-MODULES

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NIKNAM A.; SHADKAM S.

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ISSN: 2588-4824

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Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2010 | Volume:36 | Issue:2 Page(s): 209-216

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Title

CHEBYSHEV CENTERS AND APPROXIMATION IN PRE-HILBERT C*-MODULES

Author(s)

NIKNAM A. | SHADKAM S. | Issue Writer Certificate

Keywords

FARTHEST POINT

CHEBYSHEV CENTER

UNIQUELY REMOTAL SET

HILBERT C -MODULE

AVALUED NORM

Abstract

We extend the study of CHEBYSHEV CENTERs in pre-Hilbert C*-modules by considering the C*-algebra valued map defined by ½x½=<x, x>1/2. We prove that if T is a remotal subset of a pre-Hilbert C*-module M, and F Í M is star-shaped at a relative CHEBYSHEV CENTER c of T with respect to F, then ½x-qT (x)½2 ³ ½x-c½2+½c-qT (c)½2 (x Î F). The uniqueness of CHEBYSHEV CENTER follows from this inequality. This is a generalization of a well-known result on Hilbert spaces.

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APA: Copy

NIKNAM, A., & SHADKAM, S.. (2010). CHEBYSHEV CENTERS AND APPROXIMATION IN PRE-HILBERT C*-MODULES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 36(2), 209-216. SID. https://sid.ir/paper/572416/en

Vancouver: Copy

NIKNAM A., SHADKAM S.. CHEBYSHEV CENTERS AND APPROXIMATION IN PRE-HILBERT C*-MODULES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2010;36(2):209-216. Available from: https://sid.ir/paper/572416/en

IEEE: Copy

A. NIKNAM, and S. SHADKAM, “CHEBYSHEV CENTERS AND APPROXIMATION IN PRE-HILBERT C*-MODULES,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 36, no. 2, pp. 209–216, 2010, [Online]. Available: https://sid.ir/paper/572416/en

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