scholarly journals The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces

1982 ◽  
Vol 5 (2) ◽  
pp. 345-349 ◽  
Author(s):  
William V. Smith
Keyword(s):  
Duality Theory ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

This paper is devoted to a proof of the characterization without duality theory, using strong integrals, while eliminating any assumptions of barrelledness or equicontinuity.

scholarly journals A characterization of Pontryagin–van Kampen duality for locally convex spaces

2002 ◽  
Vol 121 (1-2) ◽  
pp. 75-89 ◽  
Author(s):  
Fernando Garibay Bonales ◽  
F.Javier Trigos-Arrieta ◽  
Rigoberto Vera Mendoza
Keyword(s):  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

On the Nonstandard Duality Theory of Locally Convex Spaces

1980 ◽  
Vol 32 (2) ◽  
pp. 460-479 ◽  
Author(s):  
Arthur D. Grainger
Keyword(s):  
Vector Space ◽  
Duality Theory ◽  
Dual System ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Nonstandard Model ◽  
Locally Convex ◽  
External Property ◽  
Convex Spaces

This paper continues the nonstandard duality theory of locally convex, topological vector spaces begun in Section 5 of [3]. In Section 1, we isolate an external property, called the pseudo monad, that appears to be one of the central concepts of the theory (Definition 1.2). In Section 2, we relate the pseudo monad to the Fin operation. For example, it is shown that the pseudo monad of a µ-saturated subset A of *E, the nonstandard model of the vector space E, is the smallest subset of A that generates Fin (A) (Proposition 2.7).The nonstandard model of a dual system of vector spaces is considered in Section 3. In this section, we use pseudo monads to establish relationships among infinitesimal polars, finite polars (see (3.1) and (3.2)) and the Fin operation (Theorem 3.7).

scholarly journals Characterizations of collectively precompact and semi-precompact opterators on topological vector spaces

1979 ◽  
Vol 28 (2) ◽  
pp. 179-188 ◽  
Author(s):  
M. V. Deshpande ◽  
S. M. Padhye
Keyword(s):  
Subject Classification ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Totally Bounded ◽  
Primary 47 ◽  
Bounded Sets ◽  
Locally Convex ◽  
Convex Spaces

AbstractCharacterizations of collectively precompact and collectively semi-precompact sets of operators on topological vector spaces are obtained. These lead to the characterization of totally bounded sets of semi-precompact operators on locally convex spaces.1980 Mathematics subject classification (Amer. Math. Soc): primary 47 B 05, 47 D 15; secondary 46 A 05, 46 A 15.

On ∧-Mackey convergence in locally convex spaces

1984 ◽  
Vol 96 (3) ◽  
pp. 495-500
Author(s):  
Jan H. Fourie
Keyword(s):  
Convergence Property ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Necessary And Sufficient Condition ◽  
Banach Sequence Space ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Banach Sequence ◽  
Convex Spaces

In this note we introduce the concepts of Λ-Mackey sequence, Λ-Mackey convergence property, Λ-Schwartz family and associated Λ-Schwartz family and consider some applications of these to locally convex spaces. Hereby Λ denotes a Banach sequence space with the AK-property — the results of this paper generalize those in [4] where the case Λ = I1 is considered. We obtain a dual characterization of those locally convex spaces which satisfy the Λ-Mackey convergence property and characterize the dual Λ-Schwartz spaces in terms of the SM-property which is introduced in [10]. Finally, necessary and sufficient condition for a locally convex space to be ultra-bornological is proved.

A CHARACTERIZATION OF PONTRYAGIN-VAN KAMPEN DUALITY FOR COMPLEX LOCALLY CONVEX SPACES

2002 ◽  
Vol 30 (4) ◽  
pp. 1715-1724
Author(s):  
Fernando Garibay Bonales ◽  
F. Javier Trigos-Arrieta ◽  
Rigoberto Vera Mendoza
Keyword(s):  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals A Variational McShane Characterization of Locally Convex Spaces Possessing the Radon-Nikodym Property

2014 ◽  
Vol 58 (1) ◽  
pp. 23-35
Author(s):  
Sokol Bush Kaliaj
Keyword(s):  
Lebesgue Measure ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Absolutely Continuous ◽  
Topological Vector Spaces ◽  
Nikodym Property ◽  
Interval Functions ◽  
Locally Convex ◽  
Convex Spaces

Abstract We present a characterization of complete locally convex topological vector spaces possessing the Radon-Nikodym property in terms of additive interval functions whose McShane variational measures are absolutely continuous with respect to the Lebesgue measure.

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