An Indefinite Excursion in Operator Theory

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.

• Introduces the concepts step by step and provides full proofs of all the results to make the theory accessible to readers without specialised training
• Explains the deep connections between operator theory on spaces with indefinite inner product and complex analysis
• Discusses applications in areas such as interpolation theory, dilation theory, and realisations of operator-valued functions