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Locally Convex Topological Vector Spaces
2015Locally convex topological vector spaces form an important class of topological spaces. We have already seen some examples in the previous chapter. This chapter is motivated in part by the study of the space of functions analytic in a given open set and of its dual, and by the study of spaces of test functions and of distributions (for instance the ...
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Certain locally convex topologies on the discrete vector-valued Lebesgue spaces
Periodica Mathematica Hungarica, 2012Let Γ be a set and (E, ‖·‖E) be a nontrivial Banach space. In this paper, through generalizing to vector-valued discrete Lebesgue spaces l1(Γ,E), we show that the topology β1(Γ,E) introduced by Singh is, in fact, a type of strict topology. This observation enables us to conclude various basic properties of β1(Γ,E).
Saeid Maghsoudi, Rasoul Nasr-Isfahani
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Introduction to Locally Convex Topological Vector Spaces and Dual Pairs
1984The purpose of this chapter is to provide a quick introduction to some of the basic aspects of the theory of topological vector spaces. Various versions of the Hahn-Banach theorem will be used later in the book and the exposition therefore centers around a fairly detailed treatment of these fundamental results.
Christian Berg +2 more
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Variational inequalities in locally convex Hausdorff topological vector spaces
Archiv der Mathematik, 1998A class of nonlinear variational inequalities involving strongly G-monotone mappings in a locally convex Hausdorff topological vector space setting is presented. The obtained result generalizes the results on nonlinear variational inequalities on monotone and strongly monotone mappings.
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Basic sequences and non locally convex topological vector spaces
Rendiconti del Circolo Matematico di Palermo, 1987The paper is concerned with some application of basic sequences in the theory of non-locally convex topological vector spaces. Some results of Kalton, Peck, Gregory and Shapiro are extended.
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Journal of Mathematical Sciences, 2016
For a topological vector space (X, τ), we consider the family LCT(X, τ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ. We prove that for an infinite-dimensional reflexive Banach space (X, τ), the cardinality of LCT(X, τ) is at least \( \mathfrak{c} \).
V. Tarieladze, E. Martín-Peinador
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For a topological vector space (X, τ), we consider the family LCT(X, τ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ. We prove that for an infinite-dimensional reflexive Banach space (X, τ), the cardinality of LCT(X, τ) is at least \( \mathfrak{c} \).
V. Tarieladze, E. Martín-Peinador
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The space of vector‐valued integrable functions under certain locally convex topologies
Mathematische Nachrichten, 2012AbstractLet E be a Banach space, Ω a locally compact space, and μ a positive Radon measure on Ω. In this paper, through extending to Lebesgue‐Bochner spaces, we show that the topology β1 introduced by Singh is a type of strict topology. We then investigate various properties of this locally convex topology.
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A Self‐Powered Dual‐Type Signal Vector Sensor for Smart Robotics and Automatic Vehicles
Advanced Materials, 2022Shaoxin Li, Zhihao Zhao, Di Liu
exaly
, 2021 Locally convex topologies on spaces of continuous vector functions
Mathematische Nachrichten, 1976openaire +2 more sources