An Indefinite Excursion in Operator Theory: Geometric and Spectral Treks in Kreĭn Spaces

ISBN-13: 9781108969031 / Angielski / Miękka / 2022 / 510 str.

Ankara) Aurelian Gheondea (Bilkent University

Opis

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.

Spis treści

1. Inner product spaces; 2. Angular operators; 3. Subspaces of Kreĭn spaces; 4. Linear operators on Kreĭn spaces; 5. Selfadjoint projections and unitary operators; 6. Techniques of induced Kreĭn 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.