Quantum Bounded Symmetric Domains

TL;DR

This monograph explores quantum bounded symmetric domains, offering insights into noncommutative complex analysis and expanding the understanding of quantum algebraic structures.

Contribution

It provides a comprehensive study of quantum bounded symmetric domains, including their structure and applications in noncommutative complex analysis.

Findings

Introduction of quantum bounded symmetric domains as examples in noncommutative analysis

Development of algebraic and analytical tools for these domains

Connections established between quantum domains and classical symmetric spaces

Abstract

This is Leonid Vaksman's monograph "Quantum bounded symmetric domains" (in Russian), preceded with an English translation of the table of contents and (a part) of the introduction. Quantum bounded symmetric domains are interesting from several points of view. In particular, they provide interesting examples for noncommutative complex analysis (i.e., the theory of subalgebras of C^*-algebars) initiated by W. Arveson.