Title of article :
Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules
Author/Authors :
NIKNAM, A. ferdowsi university of mashhad - Center of Excellence of Analysis on Algebraic Structure - Department of Mathematics, مشهد, ايران , SHADKAM, S. ferdowsi university of mashhad - Center of Excellence of Analysis on Algebraic Structure - Department of Mathematics, مشهد, ايران
Abstract :
We extend the study of Chebyshev centers in pre-Hilbert C*-modules by considering the C*-algebra valued map defined by |x| = (x, xi)1/2. We prove that if T is a remotal subset of a pre- Hilbert C*-module M, and F subseteq M is star-shaped at a relative Chebyshev center c of T with respect to F, then |x − qT (x)|2 geq |x−c|2 +|c−qT (c)|2(x in F). The uniqueness of Chebyshev center follows from this inequality. This is a generalization of a well-known result on Hilbert spaces
Keywords :
Farthest point , chebyshev center , uniquely remotal set , Hilbert C* , module , Avalued norm
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
