Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Hyponormal Toeplitz operators and zeros of polynomials


Author: Takahiko Nakazi
Journal: Proc. Amer. Math. Soc. 136 (2008), 2425-2428
MSC (2000): Primary 47B20, 47B35
DOI: https://doi.org/10.1090/S0002-9939-08-08752-2
Published electronically: March 7, 2008
MathSciNet review: 2390509
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The problem of hyponormality for Toeplitz operators with (trigo- nometric) polynomial symbols is studied. We give a necessary and sufficient condition using the zeros of the analytic polynomial induced by the Fourier coefficients of the symbol.


References [Enhancements On Off] (What's this?)

  • 1. C. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103(1988), 809-812.MR 0947663 (89f:47038)
  • 2. J. A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, Operator Theory: Advances and Applications, 45, Birkhäuser-Verlag, Basel, 1990. MR 1083145 (92m:47024)
  • 3. I. S. Hwang and W. Y. Lee, Hyponormality of trigonometric Toeplitz operators, Trans. Amer. Math. Soc. 354(2002), 2461-2474. MR 1888332 (2003a:47057)
  • 4. T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338(1993), 753-767. MR 1162103 (93j:47040)
  • 5. I. Schur, $ \ddot {\rm U}$ber Potenzreihen die im Innern des Einheitskreises beschr $ \ddot {\rm a}$nkt sind, J. Reine Angew. Math. 147(1917), 205-232.
  • 6. K. Zhu, Hyponormal Toeplitz operators with polynomial symbols, Integr. Equat. Oper. Th. 21(1995), 376-381. MR 1316550 (95m:47044)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B20, 47B35

Retrieve articles in all journals with MSC (2000): 47B20, 47B35


Additional Information

Takahiko Nakazi
Affiliation: Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan

DOI: https://doi.org/10.1090/S0002-9939-08-08752-2
Keywords: Trigonometric Toeplitz operators, hyponormal operator, Pick problem
Received by editor(s): December 2, 2005
Received by editor(s) in revised form: April 12, 2006
Published electronically: March 7, 2008
Additional Notes: This research was partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society

American Mathematical Society