# On the Commutativity of a Certain Class of Toeplitz Operators

Issam Louhichi; Fanilo Randriamahaleo; Lova Zakariasy

Concrete Operators (2014)

- Volume: 2, Issue: 1, page 1-10, electronic only
- ISSN: 2299-3282

## Access Full Article

top## Abstract

top## How to cite

topIssam Louhichi, Fanilo Randriamahaleo, and Lova Zakariasy. "On the Commutativity of a Certain Class of Toeplitz Operators." Concrete Operators 2.1 (2014): 1-10, electronic only. <http://eudml.org/doc/266638>.

@article{IssamLouhichi2014,

abstract = {One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.},

author = {Issam Louhichi, Fanilo Randriamahaleo, Lova Zakariasy},

journal = {Concrete Operators},

keywords = {Toeplitz operator; Mellin transform},

language = {eng},

number = {1},

pages = {1-10, electronic only},

title = {On the Commutativity of a Certain Class of Toeplitz Operators},

url = {http://eudml.org/doc/266638},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Issam Louhichi

AU - Fanilo Randriamahaleo

AU - Lova Zakariasy

TI - On the Commutativity of a Certain Class of Toeplitz Operators

JO - Concrete Operators

PY - 2014

VL - 2

IS - 1

SP - 1

EP - 10, electronic only

AB - One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.

LA - eng

KW - Toeplitz operator; Mellin transform

UR - http://eudml.org/doc/266638

ER -

## References

top- [1] P. Ahern and Z. Čučkovic, A theorem of Brown-Halmos type for Bergman space Toeplitz operators, J. Funct. Anal. 187 (2001), 200-210. Zbl0996.47037
- [2] Z. Čučkovic and N. V. Rao, Mellin transform, monomial Symbols, and commuting Toeplitz operators, J. Funct. Anal. 154 (1998), 195-214. Zbl0936.47015
- [3] I. Louhichi and N. V. Rao, Roots of Toeplitz operators on the Bergman space. Pacific Journal of Mathematics. Volume 252, Number 1 (2011), 127-144.[WoS] Zbl1237.47033
- [4] I. Louhichi and N. V. Rao, Bicommutants of Toeplitz operators, Arch. Matik. Volume 91 (2008), 256-264. Zbl1168.47026
- [5] I. Louhichi, N. V. Rao and A. Yousef, Two questions on products of Toeplitz operators on the Bergman space, Complex Analysis and Operator Theory. Volume 3, Number 4 (2009), 881-889.[WoS] Zbl1195.47018
- [6] X. Ding, A question of Toeplitz operators on the harmonic Bergman space, J. Math. Anal. Appl. 344(2008) 367 - 372. Zbl1143.47018
- [7] X. T. Dong and Z. H Zhou, Products of Toeplitz operators on the harmonic Bergman space, Proc. Amer. Math. Soc. 138, (2010), 1765-1773. Zbl1195.47014
- [8] I. Louhichi, Powers and roots of Toeplitz operators, Proc. Amer. Math. Soc. 135, (2007), 1465-1475.[WoS] Zbl1112.47023
- [9] I. Louhichi, E. Strouse and L. Zakariasy, Products of Toeplitz operators on the Bergman space, Integral equations Operator Theory 54 (2006), 525-539. Zbl1109.47023
- [10] I. Louhichi and L. Zakariasy, On Toeplitz operators with quasihomogeneous symbols, Arch. Math. 85 (2005), 248-257. Zbl1088.47019
- [11] I. Louhichi and L. Zakariasy, Quasihomogeneous Toeplitz operators on the harmonic Bergman space, Arch. Math. 98, Issue 1 (2012), 49-60.[WoS] Zbl1251.47029
- [12] R. Remmert, Classical Topics in Complex Function Theory, Graduate Texts in Mathematics, Springer, New York, 1998. Zbl0895.30001

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.