Journal ArticleDOI
Spectral Properties of Partial *-Algebras
TLDR
In this paper, the special case of partial *-algebras of operators is examined, in order to find sufficient hints for the study of the abstract case, and the outcome consists in the selection of a class of topological GC*-alges that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*algebra.Abstract:
We continue our study of topological partial *algebras focusing our attention to some basic spectral properties. The special case of partial *-algebras of operators is examined first, in order to find sufficient hints for the study of the abstract case. The outcome consists in the selection of a class of topological partial *-algebras (partial GC*-algebras) that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*-algebra.read more
Citations
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Operators in rigged Hilbert spaces: Some spectral properties
TL;DR: In this paper, a notion of resolvent set for an operator acting in a rigged Hilbert space D ⊆ H ⊂ D × is proposed, which depends on a family of intermediate locally convex spaces living between D and D ×, called interspaces.
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Operators in Rigged Hilbert spaces: some spectral properties
TL;DR: In this article, a notion of resolvent set for an operator acting in a rigged Hilbert space is proposed, which depends on a family of intermediate locally convex spaces called interspaces.
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Fully representable and *-semisimple topological partial *-algebras
TL;DR: In this paper, the authors focus on topological partial *-algebras, i.e., those that possess a multiplicative core and sufficiently many *-representations.
Journal ArticleDOI
Bounded elements of c*-inductive locally convex spaces
TL;DR: The notion of bounded element of C*-inductive locally convex spaces (or C*inductive partial *-algebras) is introduced and discussed in this article.
Journal Article
Order bounded elements of topological *-algebras
TL;DR: Several different notions of bounded elements of a topological *-algebra have been considered in this paper, and it is proved that under certain circumstances (in particular, when $\mathfrak{A}$ possesses sufficiently many *-representations) order-boundedness is equivalent to spectral boundedness.
References
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Book
Partial *- Algebras and Their Operator Realizations
TL;DR: The theory of Partial O*-Algebras has been studied extensively in the literature, see as mentioned in this paper for a detailed overview of some of the most important works on the subject.
Journal ArticleDOI
Partial *-algebras of closed linear operators in Hilbert space
Jean-Pierre Antoine,W. Karwowski +1 more
TL;DR: In this article, a corrected version of our statements has been included in another work by one of us, and the present addition to our paper results from extensive discusions, both orally and by correspondance, with Dr0 Kiirsten, Prof. G. Lassner and Dr. F. Mathot.
Partial *-algebras of closed linear operators in Hilbert space - Erratum/Addendum
Jean-Pierre Antoine,W. Karwowski +1 more
The completion of a c ⁄ -algebra with a locally convex topology
TL;DR: In this article, the structure and representation theory of a GB ⁄ -algebra with respect to a locally convex topology is investigated. But it is not known whether the multiplication of A(t) may be or not be jointly continuous.