zbMATH — the first resource for mathematics

Jordan algebras in analysis, operator theory, and quantum mechanics. (English) Zbl 0608.17013
Regional Conference Series in Mathematics 67. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-0717-X). viii, 85 p. (1987).
These notes contain the lectures given by the author at the CBMS-NSF Regional Conference at the University of California, Irvine, July 1985. They describe the applications of Jordan algebras in several areas in the general framework of JB-algebras and JB\(^*\)-triples.
The lectures are concerned with the following topics: JB-algebras and JB\(^*\)-triples, bounded symmetric domains and JB\(^*\)-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 \(C^*\)-algebras, index theory for multivariable Toeplitz operators, quantization of curved phase spaces.
Each lecture contains a vast amount of material along with an extensive bibliography.

17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
17C65 Jordan structures on Banach spaces and algebras
46H70 Nonassociative topological algebras
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
46G20 Infinite-dimensional holomorphy
46L70 Nonassociative selfadjoint operator algebras
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
81Q99 General mathematical topics and methods in quantum theory