Hermitian spectral theory, automatic continuity and locally convex *-algebras with a C*-enveloping algebra

Bhatt, Subhash J. ; Fragoulopoulou, Maria ; Inoue, Atsushi ; Karia, Dinesh J. (2007) Hermitian spectral theory, automatic continuity and locally convex *-algebras with a C*-enveloping algebra Journal of Mathematical Analysis and Applications, 331 (1). pp. 69-90. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jmaa.2006.08.062

Abstract

A considerable number of non-normed topological *-algebras admit a C*-enveloping algebra. Various characterizations of such algebras are given in terms of diverse properties of decisive features of a given topological *-algebra, like the sets of its continuous *-representations, its continuous positive functionals, the hermitian spectrum, etc. Interconnections of these sorts of algebras with hermiticity and C*-spectrality are also discussed. An analogy in structure, between (not necessarily involutive) commutative Q-algebras and topological *-algebras having a C*-enveloping algebra, leads to the study of some automatic continuity results. Furthermore, different examples are presented concerning the question: When does a dense Fréchet *-subalgebra of a C*-algebra have a C*-enveloping algebra? Some questions and conjectures are stated that arise from the whole study.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hermitian Spectral Theory; Automatic Continuity; C*-Enveloping Algebra
ID Code:59666
Deposited On:07 Sep 2011 05:21
Last Modified:07 Sep 2011 05:21

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