Abstract
Those properties of Pontrjagin spaces (Krein spaces with a finite rank of indefiniteness) and of their linear operators are considered which are not available in arbitrary Krein spaces or can there only be established by more delicate methods. In particular, Sections 4–5 give estimates for the number of non-unimodular (resp. non-real) or non-semi-simple eigenvalues of an isometric (resp. symmetric) operator, while in Sections 7–9 the investigation of invariant maximal semi-definite subspaces is carried on. Theorems 1.4, 2.2, 2.5, 3.2, 4.3, 7.3, 8.2, 9.3, 9.4 and Corollary 8.5 are worth special mentioning.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bognár, J. (1974). Pontrjagin Spaces and Their Linear Operators. In: Indefinite Inner Product Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65567-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-65567-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65569-2
Online ISBN: 978-3-642-65567-8
eBook Packages: Springer Book Archive