Homomorphisms of weighted algebras of continuous functions

Cornell University - arXiv, 2021

Journal of the Australian …, 1991

If V is a system of weights on a completely regular Hausdorff space X and £ is a locally convex space, then CV 0 (X, E) and CV b (X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

Proceedings of the London Mathematical Society, 1979

Abstract and Applied Analysis, 2014

showed that if A is the commutative Calgebra C 0 (X) with X a locally compact Hausdor¤ space, then M (C 0 (X)) = C b (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 that Hom C0(X;A) (C 0 (X; E); C 0 (X; F )) ' C s;b (X; Hom A (E; F )): (1) where E and F are p-normed spaces which are also essential isometric left Amodules with A a certain commutative F -algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

Advances in Mathematics, 2005

Let U and V be convex and balanced open subsets of the Banach spaces X and Y respectively. In this paper we study the following question: Given two Fréchet algebras of holomorphic functions of bounded type on U and V respectively that are algebra-isomorphic, can we deduce that X and Y (or X * and Y * ) are isomorphic? We prove that if X * or Y * has the approximation property and H wu (U ) and H wu (V ) are topologically algebra-isomorphic, then X * and Y * are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b (U ) and H b (V ), giving conditions under which an algebra-isomorphism between H b (X) and H b (Y ) is equivalent to an isomorphism between X * and Y * . We also obtain characterizations of different algebra-homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on H b (X) with pathological behaviors. 22 and 23. Since T * is reflexive, if U ⊂ T * and V ⊂ Y are convex and balanced open sets and H b (U ) and H b (V ) are topologically algebra-isomorphic, then T * and Y are isomorphic. Moreover, H b (T * ) and H b (Y ) are isomorphic if and only if T * and Y are isomorphic.

Contemporary Mathematics, 2003

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Acta et commentationes Universitatis Tartuensis de mathematica, 2022

Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV (0) (X, A) be the algebra of all weighted vector-valued continuous functions with the topology given by the uniform seminorms induced by V. In this paper we study some properties of A that are inherited by CV (0) (X, A). These properties are related to the unit element, spectral seminorms and uniformly A-convex property.

Proceedings Mathematical Sciences, 2002

In this note, we study homomorphisms with domain D n (X) or Lip α (X, d) of which ranges are certain Banach function algebras and determine in which cases these homomorphisms are compact.

Bulletin of the Malaysian Mathematical Sciences Society, 2014

Characterizations of multipliers on algebras of continuous functions with values in a commutative Banach or C algebra A have been obtained by several authors. In this paper, we investigate the extent to which these characterizations can be made beyond Banach algebras. We shall focus mainly on the algebras of continuous functions with values in an F algebra A (not necessarily locally convex), in particular in a complete p normed algebra, 0 < p 1, having a minimal approximate identity. We include a few examples related to our results. Most of our initial results remain valid without the commutativity of A.