scholarly journals Korovkin theory for vector-valued functions on a locally compact space

2013 ◽  
Vol 176 ◽  
pp. 23-41 ◽  
Author(s):  
Walter Roth
Keyword(s):  
Compact Space ◽  
Locally Compact ◽  
Locally Compact Space ◽  
Vector Valued Functions ◽  
Vector Valued

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

On Unsymmetric Dirichlet Forms

1973 ◽  
Vol 25 (2) ◽  
pp. 252-260 ◽  
Author(s):  
Joanne Elliott
Keyword(s):  
Compact Space ◽  
Measure Space ◽  
Closed Subspace ◽  
Finite Measure ◽  
Dirichlet Forms ◽  
Locally Compact ◽  
Locally Compact Space ◽  
Finite Measure Space

Let F be a linear, but not necessarily closed, subspace of L2[X, dm], where (X,,m) is a σ-finite measure space with the Borel subsets of the locally compact space X. If u and v are measureable functions, then v is called a normalized contraction of u if and Assume that F is stable under normalized contractions, that is, if u ∈ F and v is a normalized contraction of u, then v ∈ F.

Actions That Fiber and Vector Semigroups

1972 ◽  
Vol 24 (1) ◽  
pp. 29-37 ◽  
Author(s):  
T. H. McH. Hanson
Keyword(s):  
Compact Space ◽  
Lie Group ◽  
Fiber Bundle ◽  
Closed Subset ◽  
Locally Compact ◽  
Locally Compact Space

From [2], we can derive a criterion for determining when an action of a Lie group on a locally compact space leads to a fiber bundle. Here, we present an equivalent criterion which can be stated purely in the language of actions of groups on spaces. This is Theorem I. Using this result, we are able to give a version of a result of Home [1] for dimensions greater than one. This is done in Theorem IV and Corollary IVA. In Theorem II, we show that if a vector semigroup acts on a space X, then whenever the map t ↦ tx is 1 — 1 from onto x, it is in fact a homeomorphism. Also, is a closed subset of X. This is also a version of a result in [1].

scholarly journals The strict topology on a space of vector-valued functions

1979 ◽  
Vol 22 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Liaqat Ali Khan
Keyword(s):  
Scalar Field ◽  
Topological Space ◽  
Vector Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Strict Topology ◽  
Locally Compact ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex

Let X be a topological space, E a real or complex topological vector space, and C(X, E) the vector space of all bounded continuous E-valued functions on X. The notion of the strict topology on C(X, E) was first introduced by Buck (1) in 1958 in the case of X locally compact and E a locally convex space. In recent years a large number of papers have appeared in the literature concerned with extending the results contained in Buck's paper (1); see, for example, (14), (15), (3), (4), (12), (2), and (6). Most of these investigations have been concerned with generalising the space X and taking E to be the scalar field or a locally convex space.

ON ALGEBRAIC EQUATION WITH COEFFICIENTS FROM THE $ \beta $-UNIFORM ALGEBRA $ C_{\beta} (\Omega) $

2018 ◽  
Vol 52 (3 (247)) ◽  
pp. 161-165
Author(s):  
A.H. Kamalyan ◽  
M.I. Karakhanyan
Keyword(s):  
Algebraic Equation ◽  
Compact Space ◽  
Uniform Algebra ◽  
Locally Compact ◽  
Locally Compact Space

In this work the question of algebraic closeness of $ \beta $-uniform algebra $ A (\Omega) $ defined on locally compact space $ \Omega $ is investigated.

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.

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