Vector-Valued Functions Generated by the Operator of Finite Order and Their Application to Solving Operator Equations in Locally Convex Spaces

2018 ◽  
Vol 62 (3) ◽  
pp. 34-44
Author(s):  
S. N. Man’ko
Keyword(s):  
Finite Order ◽  
Locally Convex Spaces ◽  
Operator Equations ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex ◽  
Convex Spaces

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.

scholarly journals A note on the omega lemma

1979 ◽  
Vol 20 (3) ◽  
pp. 421-435 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Finite Order ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

A class of locally convex spaces, a B-subfamily of finite order, is defined and the omega lemma for spaces belonging to this family is proved.

scholarly journals Extension of vector-valued functions and weak–strong principles for differentiable functions of finite order

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Karsten Kruse
Keyword(s):  
Finite Order ◽  
Hausdorff Space ◽  
Linear Operators ◽  
Continuous Linear ◽  
Differentiable Functions ◽  
Weighted Banach Space ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex ◽  
Continuous Linear Operators

AbstractIn this paper we study the problem of extending functions with values in a locally convex Hausdorff space E over a field $$\mathbb {K}$$ K , which has weak extensions in a weighted Banach space $${\mathcal {F}}\nu (\Omega ,\mathbb {K})$$ F ν ( Ω , K ) of scalar-valued functions on a set $$\Omega$$ Ω , to functions in a vector-valued counterpart $$\mathcal {F}\nu (\Omega ,E)$$ F ν ( Ω , E ) of $${\mathcal {F}}\nu (\Omega ,\mathbb {K})$$ F ν ( Ω , K ) . Our findings rely on a description of vector-valued functions as continuous linear operators and extend results of Frerick, Jordá and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.

Sign in / Sign up

Export Citation Format

Share Document