IJPAM: Volume 99, No. 2 (2015)

FARTHEST POINTS IN
HILBERT OPERATOR SPACES WITH APPLICATIONS

M. Iranmanesh$^1$, F. Soleimany$^2$
$^{1,2}$Department of Mathematical Sciences
Shahrood University of Technology
P.O. Box 3619995161-316, Shahrood, IRAN


Abstract. The purpose of this paper is to Provide conditions for the existence of farthest points of closed and bounded subsets of Hilbert operator spaces. This will done by applying the concept of numerical range. We give, inter alia, some results to characterize farthest points of a subset of a $C^{\ast}$-algebra $\mathbb{A} $ from a fixed element $ x\in \mathbb{A}$. Meanwhile, we point out the main theorems of R. Saravanan and R. Vijayaragavan[#!26!#] are incorrect, by given two counterexamples.

Received: November 1, 2014

AMS Subject Classification: 41A50, 41A52, 41A65, 46L05, 47A58

Key Words and Phrases: farthest point, strong farthest point, numerical range, $C^{*} $-algebras

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DOI: 10.12732/ijpam.v99i2.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 2
Pages: 191 - 200


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