International Journal of Functional Analysis, Operator Theory and Applications
Volume 3, Issue 1, Pages 9 - 20
(June 2011)
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THE SPECTRUM OF A COMPACT ELEMENT OF A PSEUDOCOMPLETE LOCALLY CONVEX
INDUCTIVE LIMIT ALGEBRA
U. N. Bassey
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Abstract:
The set of bounded elements of a locally convex algebra is characterized as the union of certain naturally defined normed subalgebras. Pseudocomplete locally convex algebras are characterized in terms of the completeness of these subalgebras. Here we describe the spectrum of a compact element of a bounded pseudocomplete locally convex (strict) inductive limit algebra. We also prove, among other results, that compactness of a locally convex algebra is inherited by its isomorphic images. |
| Keywords and phrases: compact element, inductive limit algebra, locally convex algebra, pseudo-completeness, spectrum. |
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