## Unitary equivalence to a truncated Toeplitz operator: analytic symbols

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- by Stephan Ramon Garcia, Daniel E. Poore and William T. Ross PDF
- Proc. Amer. Math. Soc.
**140**(2012), 1281-1295 Request permission

## Abstract:

Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive, and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily equivalent to a direct sum of truncated Toeplitz operators.## References

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## Additional Information

**Stephan Ramon Garcia**- Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
- MR Author ID: 726101
- Email: Stephan.Garcia@pomona.edu
**Daniel E. Poore**- Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
- Email: dep02007@mymail.pomona.edu
**William T. Ross**- Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
- MR Author ID: 318145
- Email: wross@richmond.edu
- Received by editor(s): December 21, 2010
- Published electronically: July 22, 2011
- Additional Notes: The first author was partially supported by National Science Foundation Grant DMS-1001614.
- Communicated by: Richard Rochberg
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**140**(2012), 1281-1295 - MSC (2010): Primary 47A05, 47B35, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-2011-11060-8
- MathSciNet review: 2869112