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 - <p style="text-align: justify;">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.<br/></p>