Powers and roots of Toeplitz operators

Author:
Issam Louhichi

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1465-1475

MSC (2000):
Primary 47B35; Secondary 47L80

DOI:
https://doi.org/10.1090/S0002-9939-06-08626-6

Published electronically:
November 29, 2006

MathSciNet review:
2276656

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Abstract: We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in which commute with Toeplitz operators whose symbols are of the form .

**1.**P. Ahern, Z. Cuckovic, A Theorem of Brown-Halmos Type for Bergman Space Toeplitz Operators,*J. Funct. Anal.***187**(2001), 200-210. MR**1867348 (2002h:47040)****2.**S. Axler, Z. Cuckovic, Commuting Toeplitz operators with harmonic symbols,*Integral Equations and Operator Theory***14**(1991), 1-12.MR**1079815 (92f:47018)****3.**S. Axler, Z. Cuckovic, N. V. Rao, Commutants of analytic Toeplitz operators on the Bergman space,*Proc. Amer. Math. Soc.***128**(2000), 1951-1953.MR**1694299 (2000m:47035)****4.**A. Brown, P. Halmos, Algebraic properties of Toeplitz operators,*J. Reine Angew. Math.***213**(1964), 89-102. MR**0160136 (28:3350)****5.**Z. Cuckovic, N. V. Rao, Mellin transform, monomial symbols, and commuting Toeplitz operators,*J. Funct. Anal.***154**(1) (1998), 195-214.MR**1616532 (99f:47033)****6.**I. Louhichi, E. Strouse, L. Zakariasy, Products of Toeplitz operators on the Bergman space,*Integral Equations and Operator Theory*. Published on line: 1 October 2005.**7.**I. Louhichi, L. Zakariasy, On Toeplitz operators with quasihomogeneous symbols,*Archiv der Mathematik*. Volume**85**, Number 3 (2005), 248-257.MR**2172383 (2006e:47061)****8.**R. Remmert,*Classical Topics in Complex Function Theory,*Graduate Texts in Mathematics, Springer, New York, 1998. MR**1483074 (98g:30002)**

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Additional Information

**Issam Louhichi**

Affiliation:
UFR Mathématiques et Informatique, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France

Email:
louhichi@math.u-bordeaux1.fr

DOI:
https://doi.org/10.1090/S0002-9939-06-08626-6

Keywords:
Toeplitz operators,
Bergman space,
Mellin transform.

Received by editor(s):
March 26, 2005

Received by editor(s) in revised form:
December 20, 2005

Published electronically:
November 29, 2006

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.