On Quasi-Chebyshevity Subsets of Unital Banach Algebras (Analysis in Theory and Applications, 2018)
In this paper, first, we consider closed convex and bounded subsets ofinfinite-dimensional unital Banach algebras and show with regard to the general conditionsthat these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples ofthose algebras are given including the algebras of continuous functions on compactsets. We also see some results in $\rm{C}^*$-algebras and Hilbert $\rm{C}^*$-modules. Next, by consideringsome conditions, we study Chebyshev of subalgebras in $\rm{C}^*$-algebras.
Keywords: Best approximation; Quasi-Chebyshev sets; Pseudo-Chebyshev; $\rm{C}^∗$-algebras; Hilbert $\rm{C}^∗$-modules.