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 |
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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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