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Operator Siegel Domains

Published online by Cambridge University Press:  14 February 2012

Lawrence A. Harris
Lawrence A. Harris
Affiliation:
Department of Mathematics, University of Kentucky, Lexington
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Synopsis

A unified description and treatment is given for a large and important class of homogeneous Siegel domains in finite and infinite dimensions. These domains are shown to be linearly equivalent to generalized upper half-planes in spaces of operators having a kind of triple product structure.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 137 - 156
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Gindikin, S. G.. Analysis in homogeneous domains. Russian Math. Surveys 19 (1964), 1–89.CrossRefGoogle Scholar
2Halmos, P. R.. A Hilbert Space Problem Book (Princeton, N. J.: Van Nostrand, 1967).Google Scholar
3Harris, L. A.. Bounded symmetric homogeneous domains in infinite dimensional spaces. Lecture Notes in Mathematics 364 (Berlin: Springer, 1973), 13–40.Google Scholar
4Kaneyuki, S.. On the automorphism groups of homogeneous bounded domains. J. Fac. Sci. Univ.Tokyo Sect. 114 (1967), 89–130.Google Scholar
5Kaup, W.. Algebraic characterization of symmetric complex Banach manifolds. Math. Ann. 228 (1977), 39–64.CrossRefGoogle Scholar
6Korányi, A. and Wolf, J. A.. Realization of hermitian symmetric spaces as generalized half-planes. Ann. of Math. 81 (1965), 265–288.CrossRefGoogle Scholar
7Loos, O.. Jordan triple systems, R-spaces, and bounded symmetric domains. Bull. Amer. Math. Soc. 77 (1971), 558–561.CrossRefGoogle Scholar
8Pyatetskii-Shapiro, I. I.. The Geometry of the Classical Domains and the Theory of Automorphic Functions (Russian) Moscow: Fizmatgiz, 1961; (French transl.) Paris: Dunod, 1966; (English transl.) New York: Gordon and Breach, 1969.Google Scholar
9Rudin, W.. Functional Analysis (New York: McGraw-Hill, 1973).Google Scholar
10Størmer, E.. Positive linear maps of C *-algebras. Lecture Notes in Physics 29 (Berlin: Springer, 1974), 85–106.Google Scholar
11Topping, D. M.. Lectures on Von Neumann Algebras (London: Van Nostrand, 1971).Google Scholar
12Vigué, J.-P. Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornes symetriques. Ann. Sci. École Norm. Sup. 9 (1976), 203–282.CrossRefGoogle Scholar