Abstract
We describe bounded symmetric domains in complex Banach spaces and their biholomorphic automorphisms in terms of the underlying JB*-triple structures. Of particular interest in this context is the square root of a certain Bergman operator - we give a new description of this square root as exponential of a hermitian operator which gives better norm estimates. We do not give full proofs. These will appear elsewhere.
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References
Arazy J., Barton T.J., Friedman Y.: Operator differentiable functions. Integral Equations and Operator Theory 13, 461–487 (1990)
Barton T.J., Friedman Y.: Bounded derivations of JB*-triples. Quart. J. Math. Oxford 41, 255–268 (1990)
Barton T.J., Timoney R. M.: On biduals, preduals and ideals of JB*-triples. Math. Scand. 59, 177–191 (1986)
Bonsall F.F., Duncan J.: Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras. Cambridge Univerisity Press 1971
Braun R., Kaup W., Upmeier H.: On the automorphisms of circular and Reinhardt domains in complex Bartsch spaces. manuscripta math. 25, 97–133 (1978)
Dineen S.: Complete holomorphic vector fields on the second dual of a Banach space. Math. Scand. 59, 131–142 (1986)
Fernández A., Garcia E., Sanchez E., Siles M.: Strong regularity and generalized inverses in Jordan systems. Comm. in Algebra. 20, 1917–1936 (1992)
Friedman Y., Russo B.: The Gelfand-Naimark theorem for JB*-triples. Duke Math. J. 53, 139–148 (1986)
Harris L.A., Kaup W.: Linear algebraic groups in infinite dimensions. Illinois J. Math. 21, 666–674 (1977)
Horn G.: Characterization of the predual and ideal structure of a JBW*-triple. Math. Scand. 61, 117–133 (1987)
Isidro J.M., Kaup W.: Determining Boundary Sets of Bounded Symmetric Domains. manuscripta math. 81, 149–159 (1993)
Kaup W.: Algebraic Characterization of Symmetric Complex Banach Manifolds. Math. Ann. 228, 39–64 (1977)
Kaup W.: Uber die Klassifikation der symmetrischen Hermiteschen Mannigfaltigkeiten unendlicher Dimension I, II. Math. Ann. 257, 463–483 (1981); 262, 503–529 (1983)
Kaup W.: A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183, 503–529 (1983)
Loos O.: Bounded symmetric domains and Jordan pairs. Mathematical Lectures. Irvine: University of California at Irvine 1977
Loos O.: Jordan Pairs. Lecture Notes in Mathematics Vol. 460. Berlin-Heidelberg-New York: Springer 1975
Loos O.: Properly algebraic and spectrum-finite ideals in Jordan systems. Math. Proc. Camb. Phil. Soc. 114, 149–161 (1993)
Mellon P.: Holomorphic curvature of infinite dimensional symmetric complex Banach manifolds of compact type. Ann. Acad. Sci. Fennicae. 18, 299–306 (1993)
Sakai S.: C*-Algebras and W*-Algebras. Berlin-Heidelberg-New York: Springer 1971
Stachó L: On the spectrum of inner derivations in partial Jordan triples. Math. Scand. 66, 242–248 (1990)
Stachb L: On the algebraic classification of bounded circular domains. Proc. R. Ir. Acad. 91, 219–238 (1991)
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© 1994 Springer Science+Business Media Dordrecht
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Kaup, W. (1994). Hermitian Jordan Triple Systems and the Automorphisms of Bounded Symmetric Domains. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_34
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DOI: https://doi.org/10.1007/978-94-011-0990-1_34
Publisher Name: Springer, Dordrecht
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