Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras

After an appropriate restatement of the Gelfand-Naimark-Segal construction for topological* -algebras we prove that there exists an isomorphism among the set Cycl (A) of weakly continuous strongly cyclic* -representations of a barreled dual-separable* -algebra with unit A, the space HilbA (A*) of th...

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Autores principales: Iguri, Sergio Manuel, Castagnino, Mario Alberto G. J.
Publicado: 2008
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v49_n3_p_Iguri
http://hdl.handle.net/20.500.12110/paper_00222488_v49_n3_p_Iguri
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00222488_v49_n3_p_Iguri2023-06-08T14:48:15Z Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras Iguri, Sergio Manuel Castagnino, Mario Alberto G. J. After an appropriate restatement of the Gelfand-Naimark-Segal construction for topological* -algebras we prove that there exists an isomorphism among the set Cycl (A) of weakly continuous strongly cyclic* -representations of a barreled dual-separable* -algebra with unit A, the space HilbA (A*) of the Hilbert spaces that are continuously embedded in A* and are* -invariant under the dual left regular action of A, and the set of the corresponding reproducing kernels. We show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact. We discuss how these results can be used to describe cyclic representations on more general inner product spaces. © 2008 American Institute of Physics. Fil:Iguri, S.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Castagnino, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v49_n3_p_Iguri http://hdl.handle.net/20.500.12110/paper_00222488_v49_n3_p_Iguri
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description After an appropriate restatement of the Gelfand-Naimark-Segal construction for topological* -algebras we prove that there exists an isomorphism among the set Cycl (A) of weakly continuous strongly cyclic* -representations of a barreled dual-separable* -algebra with unit A, the space HilbA (A*) of the Hilbert spaces that are continuously embedded in A* and are* -invariant under the dual left regular action of A, and the set of the corresponding reproducing kernels. We show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact. We discuss how these results can be used to describe cyclic representations on more general inner product spaces. © 2008 American Institute of Physics.
author Iguri, Sergio Manuel
Castagnino, Mario Alberto G. J.
spellingShingle Iguri, Sergio Manuel
Castagnino, Mario Alberto G. J.
Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
author_facet Iguri, Sergio Manuel
Castagnino, Mario Alberto G. J.
author_sort Iguri, Sergio Manuel
title Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
title_short Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
title_full Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
title_fullStr Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
title_full_unstemmed Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
title_sort some remarks on the gelfand-naimark-segal representations of topological* -algebras
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v49_n3_p_Iguri
http://hdl.handle.net/20.500.12110/paper_00222488_v49_n3_p_Iguri
work_keys_str_mv AT igurisergiomanuel someremarksonthegelfandnaimarksegalrepresentationsoftopologicalalgebras
AT castagninomarioalbertogj someremarksonthegelfandnaimarksegalrepresentationsoftopologicalalgebras
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