Akshay Kumar

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math.FA2023

Reflexive extended locally convex spaces

Akshay Kumar, Varun Jindal

For an extended locally convex space (elcs) $(X, τ)$ , the authors in [10] studied the topology $τ_{u c b}$ of uniform convergence on bounded subsets of $(X, τ)$ on the dual $X^{*}$ of $(…

math.FA2023

Barreled extended locally convex spaces and Uniform boundedness principle

Akshay Kumar, Varun Jindal

For an extended locally convex space $(X, τ)$ , in [8], the authors studied the finest locally convex topology (flc topology) $τ_{F}$ on $X$ coarser than $τ$ . One can often prove facts…

math.FA2023

Dual of an extended locally convex space

Akshay Kumar, Varun Jindal

This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bound…

math.FA2022

The finest locally convex topology of an extended locally convex space

Akshay Kumar, Varun Jindal

Salas and Garcia introduced the concept of an extended locally convex space in [D. Salas and S. Tapia-Garcia. Extended seminorms and extended topological vector spaces. Topology an…