Operator Theory

Operator theory is a very wide field, with numerous facets, both applied and theoretical. In this book we focus on 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). There are deep connections with complex analysis, functional analysis, mathematical physics, electrical engineering, machine learning and physics to name a few. Fascinating new directions and connections regularly appear, such as operator spaces, free probability, and applications to hypercomplex analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and we hope you enjoy the reading, and profit from this endeavor.