On Quasi-Chebyshevity Subsets of Unital Banach Algebras

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.