An Indefinite Excursion in Operator Theory

Geometric and Spectral Treks in Kreĭn Spaces
Erscheinungsjahr 2022
ISBN: 978-1-108-96903-1
Verlag: Cambridge University Press

Buch, Englisch, Band 476, 510 Seiten, Format (B × H): 150 mm x 226 mm, Gewicht: 748 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Gheondea, Aurelian

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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

Über Autor(innen)

Gheondea, Aurelian
Aurelian Gheondea is Professor in the Department of Mathematics, Bilkent University, Ankara and Senior Researcher at the Simion Stoilow Institute of Mathematics of the Romanian Academy. Specialising in operator theory, functional analysis, and quantum operations, he has authored 78 research articles and one book and was the recipient of the annual Spiru Haret prize of the Romanian Academy.