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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonnegative unitary operators
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by K.-H. Förster and B. Nagy PDF
Proc. Amer. Math. Soc. 132 (2004), 1181-1193 Request permission

Abstract:

Unitary operators in Hilbert space map an orthonormal basis onto another. In this paper we study those that map an orthonormal basis onto itself. We show that a sequence of cardinal numbers is a complete set of unitary invariants for such an operator. We obtain a characterization of these operators in terms of their spectral properties. We show how much simpler the structure is in finite-dimensional space, and also describe the structure of certain isometries in Hilbert space.
References
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Additional Information
  • K.-H. Förster
  • Affiliation: Department of Mathematics, Technical University Berlin, Sekr. MA 6-4, Straße des 17. Juni 136, D-10623 Berlin, Germany
  • Email: foerster@math.tu-berlin.de
  • B. Nagy
  • Affiliation: Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
  • Email: bnagy@math.bme.hu
  • Received by editor(s): July 10, 2002
  • Received by editor(s) in revised form: December 30, 2002
  • Published electronically: October 3, 2003
  • Additional Notes: This work was supported by the Hungarian National Scientific Grant OTKA No. T-030042
  • Communicated by: Joseph A. Ball
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1181-1193
  • MSC (2000): Primary 47B15, 47B65
  • DOI: https://doi.org/10.1090/S0002-9939-03-07202-2
  • MathSciNet review: 2045436