New Classes of Generalized PN Spaces and Their Normability

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 , ν , τ , τ ∗ ), which are not Šerstnev spaces, in which the triangle function τ ∗ is not Archimedean can be endowed with a stru...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2017-12, Vol.42 (4), p.727-746
Main Authors: Harikrishnan, P. K., Guillén, Bernardo Lafuerza, Cho, Yeol Je, Ravindran, K. T.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 , ν , τ , 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.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-017-0218-z