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

Description

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.

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.