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

1 Citation (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

Fingerprint

Absorbing Set
Topological Vector Space
Invertible
Topological space
Boundedness
Triangle
Operator
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Harikrishnan, P. K., Guillén, B. L., Cho, Y. J., & Ravindran, K. T. (2017). New Classes of Generalized PN Spaces and Their Normability. Acta Mathematica Vietnamica, 42(4), 727-746. https://doi.org/10.1007/s40306-017-0218-z
Harikrishnan, P. K. ; Guillén, Bernardo Lafuerza ; Cho, Yeol Je ; Ravindran, K. T. / New Classes of Generalized PN Spaces and Their Normability. In: Acta Mathematica Vietnamica. 2017 ; Vol. 42, No. 4. pp. 727-746.
@article{8d4c5f2db7ff4987b15990410b58a55a,
title = "New Classes of Generalized PN Spaces and Their Normability",
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.",
author = "Harikrishnan, {P. K.} and Guill{\'e}n, {Bernardo Lafuerza} and Cho, {Yeol Je} and Ravindran, {K. T.}",
year = "2017",
month = "12",
day = "1",
doi = "10.1007/s40306-017-0218-z",
language = "English",
volume = "42",
pages = "727--746",
journal = "Acta Mathematica Vietnamica",
issn = "0251-4184",
publisher = "Springer Verlag",
number = "4",

}

Harikrishnan, PK, Guillén, BL, Cho, YJ & Ravindran, KT 2017, 'New Classes of Generalized PN Spaces and Their Normability', Acta Mathematica Vietnamica, vol. 42, no. 4, pp. 727-746. https://doi.org/10.1007/s40306-017-0218-z

New Classes of Generalized PN Spaces and Their Normability. / Harikrishnan, P. K.; Guillén, Bernardo Lafuerza; Cho, Yeol Je; Ravindran, K. T.

In: Acta Mathematica Vietnamica, Vol. 42, No. 4, 01.12.2017, p. 727-746.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New Classes of Generalized PN Spaces and Their Normability

AU - Harikrishnan, P. K.

AU - Guillén, Bernardo Lafuerza

AU - Cho, Yeol Je

AU - Ravindran, K. T.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85030308873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030308873&partnerID=8YFLogxK

U2 - 10.1007/s40306-017-0218-z

DO - 10.1007/s40306-017-0218-z

M3 - Article

VL - 42

SP - 727

EP - 746

JO - Acta Mathematica Vietnamica

JF - Acta Mathematica Vietnamica

SN - 0251-4184

IS - 4

ER -