Toeplitz operators and index theory in several complex variables
By: Harald Upmeier.
Series: Operator theory, advances and applications ;; vol. 81; Operator theory, advances and applications ;; v. 81.
Publisher: Birkhäuser Verlag; Birkhauser
Published: 1996
Place of publication: Basel; Boston
Language: eng
Number of pages: 481
Subjects: Toeplitz operators.; Index theory (Mathematics); Holomorphic functions.; Functions of several complex variables.
Description: This book gives a comprehensive treatment of Toeplitz operators arising in multivariable complex analysis. The first part describes in detail the underlying geometric structures (strongly pseudoconvex domains, Reinhardt domains, multivariable upper half-planes, symmetric domains and generalizations) as well as the harmonic analysis of the associated Hibert spaces of holomorphic functions (of Hardy or Bergman type). It is also of interest to mathematicians not primarily interested in operator theory.

The second part of the book determines the structure of Toeplitz operators, their C*-algebras and index theory, using modern techniques such as groupoid C*-algebras, co-crossed products and operator K-theory.
Notes: Includes bibliographical references (p. 462-470) and index.