New Classes of Generalized PN Spaces and Their Normability

Harikrishnan, P K and Guill´en, Bernardo Lafuerza and Cho, Yeol Je and Ravindran, K T (2017) New Classes of Generalized PN Spaces and Their Normability. Acta Mathematica Vietnamica, 42. pp. 727-746. ISSN 0251-4184

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Official URL: https://link.springer.com/article/10.1007/s40306-0...

Abstract

In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and D-boundedness in ˇ Serstnev spaces. We prove that some PN spaces (V, ν, τ, τ ∗ ), which are not ˇ Serstnev spaces, in which the triangle function τ ∗ is not Archimedean can be endowed with a structure of a topological vector space, and we give suitable example to illustrate this result. Also, we show that the topological spaces obtained in such a manner are normable under certain given conditions: some examples are given

Item Type: Article
Uncontrolled Keywords: Probabilistic normed spaces Šerstnev spaces Normability Topological vector spaces (TVS)
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 12 Sep 2017 10:05
Last Modified: 02 Dec 2017 04:31
URI: http://eprints.manipal.edu/id/eprint/149674

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