scholarly journals Some locally convex spaces of continuous vector-valued functions over a completely regular space and their duals

1976 ◽  
Vol 216 ◽  
pp. 367-367 ◽  
Author(s):  
A. Katsaras
Keyword(s):  
Regular Space ◽  
Locally Convex Spaces ◽  
Continuous Vector ◽  
Completely Regular ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals On approximation in weighted spaces of continuous vector-valued functions

1987 ◽  
Vol 29 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Liaqat Ali Khan
Keyword(s):  
Continuous Functions ◽  
Weighted Spaces ◽  
Regular Space ◽  
Local Convexity ◽  
Range Space ◽  
Completely Regular ◽  
Spaces Of Continuous Functions ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex

The fundamental work on approximation in weighted spaces of continuous functions on a completely regular space has been done mainly by Nachbin ([5], [6]). Further investigations have been made by Summers [10], Prolla ([7], [8]), and other authors (see the monograph [8] for more references). These authors considered functions with range contained in the scalar field or a locally convex topological vector space. In the present paper we prove some approximation results without local convexity of the range space.

scholarly journals Analyticity and quasi-Banach valued functions

1990 ◽  
Vol 42 (3) ◽  
pp. 369-382
Author(s):  
Antonio Bernal ◽  
Joan Cerdà
Keyword(s):  
Tensor Products ◽  
Locally Convex Spaces ◽  
Vector Valued Functions ◽  
Topological Tensor Products ◽  
Vector Valued ◽  
Locally Convex ◽  
Topological Tensor ◽  
Convex Spaces

We compare the definitions of analyticity of vector-valued functions and their connections with the topological tensor products of non-locally convex spaces.

Strict Topology on Spaces of Continuous Vector-Valued Functions

1979 ◽  
Vol 31 (4) ◽  
pp. 890-896 ◽  
Author(s):  
Seki A. Choo
Keyword(s):  
Tensor Product ◽  
Convex Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Locally Convex Space ◽  
Completely Regular ◽  
Vector Valued Functions ◽  
Bounded Continuous Functions ◽  
Vector Valued ◽  
Locally Convex

In this paper, X denotes a completely regular Hausdorff space, Cb(X) all real-valued bounded continuous functions on X, E a Hausforff locally convex space over reals R, Cb(X, E) all bounded continuous functions from X into E, Cb(X) ⴲ E the tensor product of Cb(X) and E. For locally convex spaces E and F, E ⴲ, F denotes the tensor product with the topology of uniform convergence on sets of the form S X T where S and T are equicontinuous subsets of E′, F′ the topological duals of E, F respectively ([11], p. 96). For a locally convex space G , G ′ will denote its topological dual.

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).

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

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.

Sequential Compactness of X Implies a Completeness Property for C(X)

1976 ◽  
Vol 28 (1) ◽  
pp. 207-210 ◽  
Author(s):  
M. Rajagopalan ◽  
R. F. Wheeler
Keyword(s):  
Hausdorff Space ◽  
Locally Convex Spaces ◽  
Compact Open Topology ◽  
Von Neumann ◽  
Completely Regular ◽  
Totally Bounded ◽  
Hausdorff Topological Vector Space ◽  
Sequential Compactness ◽  
Locally Convex ◽  
Convex Spaces

A locally convex Hausdorff topological vector space is said to be quasicomplete if closed bounded subsets of the space are complete, and von Neumann complete if closed totally bounded subsets are complete (equivalently, compact). Clearly quasi-completeness implies von Neumann completeness, and the converse holds in, for example, metrizable locally convex spaces. In this note we obtain a class of locally convex spaces for which the converse fails. Specifically, let X be a completely regular Hausdorff space, and let CC(X) denote the space of continuous real-valued functions on X, endowed with the compact-open topology.

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