Indefinite Metric spaces
Keywords:
Hilbert space, indefinite metric, Pontryagin spaces, Krein spaces, linear operators.Abstract
A conceptual historical overview around some moments of indefinite inner product spaces emphasazing basic aspects of the geometry of Krein and Pontryagin spaces is made.
References
Bognar, J,: Indefinite Inner Product space.Berlin-New York: Springer-Verlag 1974.
Bruzual, R.: Espacios con m ́etrica indefida.Laboratorio de Formas en Grupos, Centro de Analisis, Escuela de Matem ́aticas, Universidad Central de Venezuela, Septiembre 2007.
Dritschel M., Rovnyak J., Theorems for Contraction operators on Krein Spaces, Operator Theory. Advances and Applications. Vol.47, Birkhauser Verlag, Basel, 1990.
Iohvidov,I.S: Unitary operators in a space with an indefinite metric. Zap. Mat. Otd. Fiz-Mat. Fak. iHar’kov. Mat. Obsc. (4) 21, 79-86 (1949) [Russian]
Iohvidov,I.S., Krein, M.G.: Spectral theory of operators in spaces with an indefinite metric. I. TrudyMoskov. Mat. Obsc. 5. 367-432 (1957) [Russian]
Krein, M.G.:An application of the fixed-point principle in the theory of linear transformations of spaces with an indefinite metric. Upehi Mat. Nauk 5, no. 2, 180-190 (1950) [Russian]
L. de Branges: Complementation in Krein spaces. Trans. American Math Soc. 305 (1988), 277-291.
Langer, H.: On J-hermitian operators. Dokl. Akad. Nauk SSSR 134, 263-266 (1960) [Russian].
Langer, H.: Invariante Teilr ́aume definisierbarer J-selbstadjungierter operatoren. Ann. Akad. Sci. Fenn. Ser. A.I, no. 475 (1971).
Langer M., Luger A.: Operator theory: advances and applications. On norms indefinite in inner product spaces. Vol 198, Birkh auser verlag, Basel, pags. 259-264 (2009) [Suiza]
Pesonen, E.: Uber die spektraldarstellung quadratischer Formen in linearen Raumen mit indefiniter Metrik. Ann. Acad. Sci. Fenn. Ser. AI, no. 227 (1956)
Pontryagin, L.S.: Hermitian operators in spaces with indefinite metric. Izv. Akad. Nauk SSSR Ser. Mat. 8, 243-280 (1944) [Russian]
Schwarz.: Sous-espaces hilbertiens d ́espaces vectoriels topologiques et noyaux associ ́es (noyauxr eproduisants) J. Analyse Math. 13 (1964),115-256 .
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