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Homomorphisms Between Algebras of Continuous Functions

Published online by Cambridge University Press:  20 November 2018

J. G. Llavona  and
J. A. Jaramillo
J. G. Llavona
Affiliation:
Universidad Complutense, Madrid, Spain
J. A. Jaramillo
Affiliation:
Universidad Complutense, Madrid, Spain
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We are concerned in this paper with the study of homomorphisms between different algebras of continuous functions, especially the algebras of real functions which are either weakly continuous on bounded sets or weakly uniformly continuous on bounded sets on a Banach space (see definitions below).

These spaces of weakly [uniformly] continuous functions appeared in relation with some questions in Infinite-dimensional Approximation Theory (see [4], [6], [11], [12], [13] and [16]); and since the structure of these function spaces is closely related with properties of different weak topologies (the bounded-weak and bounded-weak* topologies, respectively) and with the structure of Banach spaces on which they are defined, their study also presents interest from the point of view of Banach space theory, as can be seen in [2], [12] or [17].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 1 , 01 February 1989 , pp. 132 - 162
Copyright
Copyright © Canadian Mathematical Society 1989

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