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

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Iran



 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) $.


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