TY - JOUR T1 - On Quasi-Chebyshevity Subsets of Unital Banach Algebras JO - Analysis in Theory and Applications VL - 1 SP - 92 EP - 102 PY - 2018 DA - 2018/07 SN - 34 DO - http://doi.org/10.4208/ata.2018.v34.n1.7 UR - https://global-sci.org/intro/article_detail/ata/12547.html KW - Best approximation, Quasi-Chebyshev sets, Pseudo-Chebyshev, $\rm{C}^∗$-algebras, Hilbert $\rm{C}^∗$-modules. AB -

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.