Cited by
- BibTex
- RIS
- TXT
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.
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.