Author = Taheri, Morteza

Introduction and Different Properties of Space c(I): Diameter Norm Study

Volume 9, Issue 1, 2022, Pages 37-48

https://doi.org/10.22072/wala.2022.543538.1354

Morteza Taheri, Ali Bayati Eshkaftaki

Abstract  In this paper, the space  $ c (I) $  is introduced and some of its properties examined. Then with the help of a diameter norm  on the space  $ c_{0}(I)$, a norm is defined on the space $ c (I) $ called as D- norm, which  is an extension of  the $ d-$norm. It is also shown that the D- norm is equivalent to the supremum norm.  The extreme points of the unit ball of the spaces $ c_{0}(I) $  and  $ c (I) $ are also specified. In addition we find  some orthogonal vectors in the space $ c (I) $.