Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 92–102
Abstract
In this paper, first, we consider closed convex and bounded subsets of
infinite-dimensional unital Banach algebras and show with regard to the general conditions
that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of
those algebras are given including the algebras of continuous functions on compact
sets. We also see some results in $\rm{C}^*$-algebras and Hilbert $\rm{C}^*$-modules. Next, by considering
some conditions, we study Chebyshev of subalgebras in $\rm{C}^*$-algebras.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2018.v34.n1.7
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 92–102
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Best approximation Quasi-Chebyshev sets Pseudo-Chebyshev $\rm{C}^∗$-algebras Hilbert $\rm{C}^∗$-modules.