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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

B. Nagy
Affiliation: Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

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