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Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics
Harald Upmeier
A co-publication of the AMS and CBMS.

CBMS Regional Conference Series in Mathematics
1987; 85 pp; softcover
Number: 67
ISBN-10: 0-8218-0717-X
ISBN-13: 978-0-8218-0717-0
List Price: US$24
Member Price: US$19.20
All Individuals: US$19.20
Order Code: CBMS/67
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This book is based on the CBMS Regional Conference held at the University of California, Irvine, in July 1985. Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. The author describes some relevant results and puts them in a general framework, based on the concepts of \(JB\)-algebra and \(JB^\ast\)-triple.


Table of Contents

  • \(JB\)-algebras and \(JB^\ast\)-triples
  • Bounded symmetric domains and \(JB^\ast\)-triples
  • Siegel domains and Cayley transformations
  • Geometry of Jordan structures and quantum mechanics
  • Derivations and dynamical systems
  • Kernel functions and harmonic analysis
  • Harmonic functions and Hua operators
  • Toeplitz operators and Toeplitz \(C^\ast\)-algebras
  • Index theory for multivariable Toeplitz operators
  • Quantization of curved phase spaces
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