New Classes of Generalized PN Spaces and Their Normability

P. K. Harikrishnan, Bernardo Lafuerza Guillén, Yeol Je Cho, K. T. Ravindran

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and D-boundedness in Šerstnev spaces. We prove that some PN spaces (V,τ), which are not Šerstnev 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.

Original languageEnglish
Pages (from-to)727-746
Number of pages20
JournalActa Mathematica Vietnamica
Volume42
Issue number4
DOIs
Publication statusPublished - 01-12-2017

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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