Alpay D. Operator Theory 2015

Textbook in PDF format

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Preface.
Reproducing Kernel Hilbert Spaces.
Indefinite Inner Product Spaces.
de Branges Spaces.
Linear Systems Theory.
Multivariable Operator Theory.
Infinite Dimensional Analysis.
General Aspects of Quaternionic and Clifford Analysis.
Further Developments of Quaternionic and Clifford Analysis.
Index