Proceedings of the American Mathematical Society

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Regularity of operators on essential extensions of the compacts


Author: Arupkumar Pal
Journal: Proc. Amer. Math. Soc. 128 (2000), 2649-2657
MSC (1991): Primary 46H25, 47C15
Published electronically: February 28, 2000
MathSciNet review: 1705741
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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 [Enhancements On Off] (What's this?)

  • [1] Jacques Dixmier, 𝐶*-algebras, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett; North-Holland Mathematical Library, Vol. 15. MR 0458185
  • [2] Michel Hilsum, Fonctorialité en 𝐾-théorie bivariante pour les variétés lipschitziennes, 𝐾-Theory 3 (1989), no. 5, 401–440 (French, with English summary). MR 1050489, 10.1007/BF00534136
  • [3] E. C. Lance, Hilbert 𝐶*-modules, London Mathematical Society Lecture Note Series, vol. 210, Cambridge University Press, Cambridge, 1995. A toolkit for operator algebraists. MR 1325694
  • [4] Pal, A. : On Some Quantum Groups and Their Representations, Ph. D. Thesis, Indian Statistical Institute, 1995.
  • [5] Pal, A. : Regular operators on Hilbert $C^*$-modules, Preprint, 1997, (to appear in the Journal of Operator Theory).
  • [6] Gert K. Pedersen, 𝐶*-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
  • [7] S. L. Woronowicz, Unbounded elements affiliated with 𝐶*-algebras and noncompact quantum groups, Comm. Math. Phys. 136 (1991), no. 2, 399–432. MR 1096123
  • [8] S. L. Woronowicz, 𝐶*-algebras generated by unbounded elements, Rev. Math. Phys. 7 (1995), no. 3, 481–521. MR 1326143, 10.1142/S0129055X95000207

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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: http://dx.doi.org/10.1090/S0002-9939-00-05611-2
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
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society