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.

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 Weak convergence of vector-valued series and integrals

1963 ◽  
Vol 3 (2) ◽  
pp. 159-166
Author(s):  
R. E. Edwards
Keyword(s):  
Weak Convergence ◽  
Locally Convex Spaces ◽  
Linear Forms ◽  
Vector Valued ◽  
Locally Convex ◽  
Convex Spaces

Throughout this paper E, F and G denote separated locally convex spaces, F C G, the injection i: F → G being continuous (i.e. the topology on F is finer than that induced on it by the topology on G). E′, F′ and G′ denote the respective duals of E, F and G. i′ is the adjoint map of G′ into F', which is defined by restricting linear forms on G to F C G.

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