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.
N1 - Publisher Copyright:
© 2017, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
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.
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U2 - 10.1007/s40306-017-0218-z
DO - 10.1007/s40306-017-0218-z
M3 - Article
AN - SCOPUS:85030308873
SN - 0251-4184
VL - 42
SP - 727
EP - 746
JO - Acta Mathematica Vietnamica
JF - Acta Mathematica Vietnamica
IS - 4
ER -