Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 347-367.

Krein Spaces Induced by Symmetric Operators

Authors: Petru Cojuhari (1), and Aurelian Gheondea (2)
Author institution: (1) Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickievicza 30, 30-059 Cracow, Poland
(2) Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey, and Institutul de Matematica al Academiei Romane, C.P. 1-764, 014700 Bucuresti, Romania

Summary: We introduce the notion of Krein space induced by a densely defined symmetric operator in a Hilbert space, as an abstract notion of indefinite energy spaces. Characterizations of existence and uniqueness, as well as certain canonical representations, are obtained. We exemplify these by the free and certain perturbed Dirac operators.

Keywords: Krein space, induced Krein space, Dirac operator

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