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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Regularity of operators on essential extensions of the compacts

Author(s): Arupkumar Pal
Journal: Proc. Amer. Math. Soc. 128 (2000), 2649-2657.
MSC (1991): Primary 46H25, 47C15
Posted: February 28, 2000
MathSciNet review: 1705741
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Abstract | References | Similar articles | Additional information

Abstract:

A semiregular operator on a Hilbert $C^*$-module, or equivalently, on the $C^*$-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian $C^*$-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed.

References:

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Dixmier, J. : $C^*$-Algebras, North-Holland, 1977. MR 56:16388
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Hilsum, M. : Fonctorialité en K-théory bivariante pour les variétés lipschitziennes, $K$-Theory, 3(1989), 401-440.MR 91j:19012
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Lance, E. C. : Hilbert $C^*$-modules - A Toolkit for Operator Algebraists, Cambridge University Press, 1995.MR 96k:46100
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Pal, A. : On Some Quantum Groups and Their Representations, Ph. D. Thesis, Indian Statistical Institute, 1995.
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Pal, A. : Regular operators on Hilbert $C^*$-modules, Preprint, 1997, (to appear in the Journal of Operator Theory).
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Pedersen, G.K. : $C^*$-algebras and Their Automorphism Groups, Academic Press, 1979.MR 81e:46037
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Woronowicz, S.L. : Unbounded Elements Affiliated With $C^*$-algebras and Noncompact Quantum Groups, Comm. Math. Phys., 136(1991), 399-432.MR 92b:46117
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Woronowicz, S.L. : $C^*$-algebras generated by unbounded elements, Rev. Math. Phys., 7(1995), No. 3, 481-521.MR 96c:46056

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Additional Information:

Arupkumar Pal
Affiliation: Indian Statistical Institute, 7, SJSS Marg, New Delhi--110016, India
Email: arup@isid.ac.in

DOI: 10.1090/S0002-9939-00-05611-2
PII: S 0002-9939(00)05611-2
Keywords: Hilbert $C^*$-modules, regular operators, $C^*$-algebras, essential extensions
Received by editor(s): June 29, 1998,
Received by editor(s) in revised form: October 22, 1998
Posted: February 28, 2000
Additional Notes: The author was partially supported by the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India.
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society




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