Separately continuous functions on products of locally convex spaces with the weak topology

1999 ◽  
Vol 96 (1) ◽  
pp. 2816-2820
Author(s):  
V. V. Mikhailyuk
Keyword(s):  
Weak Topology ◽  
Continuous Functions ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Operators on locally convex spaces of vector-valued continuous functions

1987 ◽  
Vol 36 (2) ◽  
pp. 267-278
Author(s):  
A. García López
Keyword(s):  
Hausdorff Space ◽  
Continuous Operator ◽  
Continuous Functions ◽  
Special Treatment ◽  
Locally Convex Spaces ◽  
Uniform Topology ◽  
Zero Sequence ◽  
Vector Valued ◽  
Locally Convex ◽  
Convex Spaces

Let E and F be locally convex spaces and let K be a compact Hausdorff space. C(K,E) is the space of all E-valued continuous functions defined on K, endowed with the uniform topology.Starting from the well-known fact that every linear continuous operator T from C(K,E) to F can be represented by an integral with respect to an operator-valued measure, we study, in this paper, some relationships between these operators and the properties of their representing measures. We give special treatment to the unconditionally converging operators.As a consequence we characterise the spaces E for which an operator T defined on C(K,E) is unconditionally converging if and only if (Tfn) tends to zero for every bounded and converging pointwise to zero sequence (fn) in C(K,E).

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.

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 .

scholarly journals On topological properties of Fréchet locally convex spaces with the weak topology

2015 ◽  
Vol 192 ◽  
pp. 123-137 ◽  
Author(s):  
S.S. Gabriyelyan ◽  
J. Ka̧kol ◽  
A. Kubzdela ◽  
M. Lopez-Pellicer
Keyword(s):  
Weak Topology ◽  
Locally Convex Spaces ◽  
Topological Properties ◽  
Locally Convex ◽  
Convex Spaces

Eberlein compacts and spaces of continuous functions

1979 ◽  
Vol 85 (2) ◽  
pp. 305-313
Author(s):  
Richard J. Hunter ◽  
J. W. Lloyd
Keyword(s):  
Topological Space ◽  
Weak Topology ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Locally Convex Spaces ◽  
Weakly Compact ◽  
Spaces Of Continuous Functions ◽  
Eberlein Compact ◽  
Necessary And Sufficient ◽  
Locally Convex

AbstractLet X be a Hausdorff topological space. We consider various locally convex spaces of continuous real valued functions on X and give necessary and sufficient conditions in order that (i) they contain an absolutely convex weakly compact total subset and (ii) they contain an absolutely convex total subset which is an Eberlein compact, when given the weak topology.

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