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

Document Type : Research Paper

Authors

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

10.22072/wala.2022.543538.1354

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) $.

Keywords

References

[1] A. Bayati Eshkaftaki, D-Norm and isometries on $c_{0}$ spaces, Oper. Matrices, 41 (2017), 1141-1148.
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[3] C. Sánchez, Diameter preserving linear maps and isometries, Arch. Math., 73 (1999), 373-379.
[4] G.M. Church, Extreme Points in Banach Spaces, Oklahoma State University, 1974.
[5] J. Hagler, Counterexample to several questions about Banach spaces, Stud. Math., 3 (1977), 289-308.
Wavelet and Linear Algebra
Volume 9, Issue 1
Autumn- Winter
2022
Pages 37-48

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