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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Iwasawa decompositions of some infinite-dimensional Lie groups


Author: Daniel Beltita
Journal: Trans. Amer. Math. Soc. 361 (2009), 6613-6644
MSC (2000): Primary 22E65; Secondary 22E46, 47B10, 47L20, 58B25
Published electronically: July 22, 2009
MathSciNet review: 2538608
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Abstract: We set up an abstract framework that allows the investigation of Iwasawa decompositions for involutive infinite-dimensional Lie groups modeled on Banach spaces. This provides a method to construct Iwasawa decompositions for classical real or complex Banach-Lie groups associated with the Schatten ideals $ \mathfrak{S}_p(\mathcal{H})$ on a complex separable Hilbert space $ \mathcal{H}$ if $ 1<p<\infty$.


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Additional Information

Daniel Beltita
Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
Email: Daniel.Beltita@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04824-7
PII: S 0002-9947(09)04824-7
Keywords: Classical Lie group; Iwasawa decomposition; operator ideal; triangular integral
Received by editor(s): February 11, 2008
Published electronically: July 22, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.