Geometry of -Stiefel manifolds

Author:
Eduardo Chiumiento

Journal:
Proc. Amer. Math. Soc. **138** (2010), 341-353

MSC (2000):
Primary 22E65; Secondary 47B10, 58B20

DOI:
https://doi.org/10.1090/S0002-9939-09-10080-1

Published electronically:
August 28, 2009

MathSciNet review:
2550200

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a separable Banach ideal in the space of bounded operators acting in a Hilbert space and the Banach-Lie group of unitary operators which are perturbations of the identity by elements in . In this paper we study the geometry of the unitary orbits

**1.**Esteban Andruchow and Gustavo Corach,*Metrics in the set of partial isometries with finite rank*, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.**16**(2005), no. 1, 31–44 (English, with English and Italian summaries). MR**2225921****2.**Esteban Andruchow and Gustavo Corach,*Differential geometry of partial isometries and partial unitaries*, Illinois J. Math.**48**(2004), no. 1, 97–120. MR**2048217****3.**E. Andruchow, G. Corach, and M. Mbekhta,*On the geometry of generalized inverses*, Math. Nachr.**278**(2005), no. 7-8, 756–770. MR**2141955**, https://doi.org/10.1002/mana.200310270**4.**J. Avron, R. Seiler, and B. Simon,*The index of a pair of projections*, J. Funct. Anal.**120**(1994), no. 1, 220–237. MR**1262254**, https://doi.org/10.1006/jfan.1994.1031**5.**Daniel Beltiţă,*Smooth homogeneous structures in operator theory*, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, vol. 137, Chapman & Hall/CRC, Boca Raton, FL, 2006. MR**2188389****6.**Daniel Beltiţă, Tudor S. Ratiu, and Alice Barbara Tumpach,*The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits*, J. Funct. Anal.**247**(2007), no. 1, 138–168. MR**2319757**, https://doi.org/10.1016/j.jfa.2007.03.001**7.**A. L. Carey,*Some homogeneous spaces and representations of the Hilbert Lie group 𝒰(ℋ)₂*, Rev. Roumaine Math. Pures Appl.**30**(1985), no. 7, 505–520. MR**826232****8.**I. C. Gohberg and M. G. Kreĭn,*Introduction to the theory of linear nonselfadjoint operators*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR**0246142****9.**P. R. Halmos and J. E. McLaughlin,*Partial isometries*, Pacific J. Math.**13**(1963), 585–596. MR**0157241****10.**Serge Lang,*Introduction to differentiable manifolds*, 2nd ed., Universitext, Springer-Verlag, New York, 2002. MR**1931083****11.**Luis E. Mata-Lorenzo and Lázaro Recht,*Infinite-dimensional homogeneous reductive spaces*, Acta Cient. Venezolana**43**(1992), no. 2, 76–90 (English, with English and Spanish summaries). MR**1185114****12.**Mostafa Mbekhta and Şerban Strǎtilǎ,*Homotopy classes of partial isometries in von Neumann algebras*, Acta Sci. Math. (Szeged)**68**(2002), no. 1-2, 271–277. MR**1916580****13.**Iain Raeburn,*The relationship between a commutative Banach algebra and its maximal ideal space*, J. Functional Analysis**25**(1977), no. 4, 366–390. MR**0458180****14.**Ioana Serban and Flavius Turcu,*Compact perturbations of isometries*, Proc. Amer. Math. Soc.**135**(2007), no. 4, 1175–1180. MR**2262923**, https://doi.org/10.1090/S0002-9939-06-08586-8**15.**Şerban Strătilă and Dan Voiculescu,*On a class of KMS states for the unitary group 𝑈(∞)*, Math. Ann.**235**(1978), no. 1, 87–110. MR**0482248**, https://doi.org/10.1007/BF01421594

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Additional Information

**Eduardo Chiumiento**

Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Calles 50 y 115, (1900) La Plata, Argentina

Email:
eduardo@mate.unlp.edu.ar

DOI:
https://doi.org/10.1090/S0002-9939-09-10080-1

Keywords:
Partial isometry,
Banach ideal,
Finsler metric

Received by editor(s):
September 18, 2008

Received by editor(s) in revised form:
April 22, 2009

Published electronically:
August 28, 2009

Communicated by:
Marius Junge

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.