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New Classes of Generalized PN Spaces and Their Normability
P. K. Harikrishnan
,
Bernardo Lafuerza Guillén
,
Yeol Je Cho
,
K. T. Ravindran
Abstract
In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and $\mathcal D$-boundedness in Šerstnev spaces. We prove that some PN spaces $(V,\nu,\tau,\tau^*)$, which are not Šerstnev spaces, in which the triangle function $\tau^*$ 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.