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Abstract:

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.

Registro:

Documento: Artículo
Título:Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras
Autor:Iguri, S.M.; Castagnino, M.A.
Filiación:Instituto de Astronomía y Física del Espacio (CONICET-UBA), C. C. 67-Suc. 28, 1428 Buenos Aires, Argentina
Dpto. de Física, FCEyN, Ciudad Universitaria Pab. I, 1428 Buenos Aires, Argentina
Año:2008
Volumen:49
Número:3
DOI: http://dx.doi.org/10.1063/1.2897032
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.
ISSN:00222488
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00222488_v49_n3_p_Iguri.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v49_n3_p_Iguri

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Citas:

---------- APA ----------
Iguri, S.M. & Castagnino, M.A. (2008) . Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras. Journal of Mathematical Physics, 49(3).
http://dx.doi.org/10.1063/1.2897032
---------- CHICAGO ----------
Iguri, S.M., Castagnino, M.A. "Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras" . Journal of Mathematical Physics 49, no. 3 (2008).
http://dx.doi.org/10.1063/1.2897032
---------- MLA ----------
Iguri, S.M., Castagnino, M.A. "Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras" . Journal of Mathematical Physics, vol. 49, no. 3, 2008.
http://dx.doi.org/10.1063/1.2897032
---------- VANCOUVER ----------
Iguri, S.M., Castagnino, M.A. Some remarks on the Gelfand-Naimark-Segal representations of topological* -algebras. J. Math. Phys. 2008;49(3).
http://dx.doi.org/10.1063/1.2897032