This modern introduction to operator theory on spaces with indefinite inner product guides the reader step by step through the important results of recent decades. It is highly readable and contains generous background material, making it suitable for graduate students and researchers in operator theory, functional analysis, and related areas.
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.
Daugiau informacijos
Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
1. Inner product spaces;
2. Angular operators;
3. Subspaces of Kren
spaces;
4. Linear operators on Kren spaces;
5. Selfadjoint projections and
unitary operators;
6. Techniques of induced Kren 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.
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.
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