A topological group characterization of those locally convex spaces having their weak topology

1971 ◽  
Vol 195 (2) ◽  
pp. 330-331 ◽  
Author(s):  
Sidney A. Morris
Keyword(s):  
Topological Group ◽  
Weak Topology ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

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

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 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.

A Topological Transversality Theorem For Multi-Valued Maps In Locally Convex Spaces With Applications To Neutral Equations

1992 ◽  
Vol 44 (5) ◽  
pp. 1003-1013 ◽  
Author(s):  
Tomasz Kaczynski ◽  
Jianhong Wu
Keyword(s):  
Sobolev Space ◽  
Weak Topology ◽  
Functional Differential Equations ◽  
Locally Convex Spaces ◽  
Compactness Property ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Locally Convex ◽  
Convex Spaces

AbstractThe concept of essential map and topological transversality due to A. Granas is extended to multi-valued maps in locally convex spaces and it is next applied to prove the solvability of boundary value problems for certain neutral functional differential equations. In order to achieve a required compactness property, the weak topology in a Sobolev space is considered. The topological tool established in the first part of the paper allows to avoid some obstacles which are encountered when trying to use standard degree-theoretical arguments.

scholarly journals On strong lifting compactness, with applications to topological vector spaces

1986 ◽  
Vol 41 (2) ◽  
pp. 211-223 ◽  
Author(s):  
A. G. A. G. Babiker ◽  
G. Heller ◽  
W. Strauss
Keyword(s):  
Structural Properties ◽  
Weak Topology ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Hausdorff Spaces ◽  
Topological Vector Spaces ◽  
Completely Regular ◽  
Locally Convex ◽  
Convex Spaces

AbstractThe notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.

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.

An invariant theorem in duality

2010 ◽  
Vol 47 (3) ◽  
pp. 299-310
Author(s):  
Yunyan Yang ◽  
Ronglu Li
Keyword(s):  
Convex Space ◽  
Weak Topology ◽  
Absolute Convergence ◽  
Convergent Series ◽  
Dual Pair ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

The concept of absolute convergence for series is generalized to locally convex spaces and an invariant theorem for absolutely convergent series in duality is established: when a locally convex space X is weakly sequentially complete, an admissible topology which is strictly stronger than the weak topology on X in the dual pair ( X,X′ ) is given such that it has the same absolutely convergent series as the weak topology in X .

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
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