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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonnegative unitary operators


Authors: K.-H. Förster and B. Nagy
Journal: Proc. Amer. Math. Soc. 132 (2004), 1181-1193
MSC (2000): Primary 47B15, 47B65
Published electronically: October 3, 2003
MathSciNet review: 2045436
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07202-2
PII: S 0002-9939(03)07202-2
Keywords: Unitary operator, infinite matrix with nonnegative entries, complete set of unitary invariants, multiplicity
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
Article copyright: © Copyright 2003 American Mathematical Society