## Nonnegative unitary operators

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- by K.-H. Förster and B. Nagy
- Proc. Amer. Math. Soc.
**132**(2004), 1181-1193 - DOI: https://doi.org/10.1090/S0002-9939-03-07202-2
- Published electronically: October 3, 2003
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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.## References

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## Bibliographic 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