On the Commutativity of a Certain Class of Toeplitz Operators

• Autorzy: Issam Louhichi , Fanilo Randriamahaleo , Lova Zakariasy
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Toeplitz operator; Mellin transform

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

wydano

2014-01-01

otrzymano

2014-01-31

zaakceptowano

2014-04-01

online

2014-05-01

Twórcy

autor

Issam Louhichi

• King Fahd University of Petroleum & Minerals, Department of Mathematics & Statistics, Dhahran 31261, Saudi Arabia

autor

Fanilo Randriamahaleo

• Université de Bordeaux, UFR de Mathématiques et Informatique, 351, Cours de la Libération, 33405 Talence, France

autor

Lova Zakariasy

• High Institute of Technology, Industrial Engineering Department, 201 Antsiranana, Madagascar

Bibliografia

• [1] P. Ahern and Z. Čučkovic, A theorem of Brown-Halmos type for Bergman space Toeplitz operators, J. Funct. Anal. 187 (2001), 200-210.
• [2] Z. Čučkovic and N. V. Rao, Mellin transform, monomial Symbols, and commuting Toeplitz operators, J. Funct. Anal. 154 (1998), 195-214.
• [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]
• [4] I. Louhichi and N. V. Rao, Bicommutants of Toeplitz operators, Arch. Matik. Volume 91 (2008), 256-264.
• [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]
• [6] X. Ding, A question of Toeplitz operators on the harmonic Bergman space, J. Math. Anal. Appl. 344(2008) 367 - 372.
• [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.
• [8] I. Louhichi, Powers and roots of Toeplitz operators, Proc. Amer. Math. Soc. 135, (2007), 1465-1475.[WoS]
• [9] I. Louhichi, E. Strouse and L. Zakariasy, Products of Toeplitz operators on the Bergman space, Integral equations Operator Theory 54 (2006), 525-539.
• [10] I. Louhichi and L. Zakariasy, On Toeplitz operators with quasihomogeneous symbols, Arch. Math. 85 (2005), 248-257.
• [11] I. Louhichi and L. Zakariasy, Quasihomogeneous Toeplitz operators on the harmonic Bergman space, Arch. Math. 98, Issue 1 (2012), 49-60.[WoS]
• [12] R. Remmert, Classical Topics in Complex Function Theory, Graduate Texts in Mathematics, Springer, New York, 1998.

Identyfikatory

DOI

10.2478/conop-2014-0001