Volume 34, Issue 1
On Quasi-Chebyshevity Subsets of Unital Banach Algebras

M. Iranmanesh & F. Soleimany

Anal. Theory Appl., 34 (2018), pp. 92-102.

Published online: 2018-07

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  • 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.

  • Keywords

Best approximation, Quasi-Chebyshev sets, Pseudo-Chebyshev, $\rm{C}^∗$-algebras, Hilbert $\rm{C}^∗$-modules.

  • AMS Subject Headings

41A50, 41A65, 41A99, 46L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-34-92, author = {}, title = {On Quasi-Chebyshevity Subsets of Unital Banach Algebras}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {1}, pages = {92--102}, 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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2018.v34.n1.7}, url = {http://global-sci.org/intro/article_detail/ata/12547.html} }
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.

M. Iranmanesh & F. Soleimany. (1970). On Quasi-Chebyshevity Subsets of Unital Banach Algebras. Analysis in Theory and Applications. 34 (1). 92-102. doi:10.4208/ata.2018.v34.n1.7
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