An Indefinite Excursion in Operator Theory
Geometric and Spectral Treks in Kre?n Spaces

Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.

Aurelian Gheondea (Author)

9781108969031, Cambridge University Press

Paperback / softback, published 28 July 2022

510 pages
22.8 x 15.1 x 2.8 cm, 0.74 kg

This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.

1. Inner product spaces
2. Angular operators
3. Subspaces of Kre?n spaces
4. Linear operators on Kre?n spaces
5. Selfadjoint projections and unitary operators
6. Techniques of induced Kre?n spaces
7. Plus/minus-operators
8. Geometry of contractive operators
9. Invariant maximal semidefinite subspaces
10. Hankel operators and interpolation problems
11. Spectral theory for selfadjoint operators
12. Quasi-contractions
13. More on definitisable operators
Appendix
References
Symbol index
Subject index.

Subject Areas: Calculus & mathematical analysis [PBK]