Result: ROOTS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

Title:
ROOTS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
Authors:
LOUHICHI, Issam, RAO, N. V
Source:
Pacific journal of mathematics. 252(1):127-144
Publisher Information:
Berkeley, CA: University of California, Department of Mathematics, 2011.
Publication Year:
2011
Physical Description:
print, 1/4 p
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Analyse fonctionnelle, Functional analysis, Théorie des opérateurs, Operator theory, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Disque, Disk, Disco, Espace linéaire, Linear space, Espacio lineal, Opérateur Toeplitz, Toeplitz operator, Operador Toeplitz, Puissance, Power, Potencia, Théorie opérateur, Operator theory, 32A36, 46Axx, 47B35, 47XX, Espace Bergman, Espace fermeture, Espace opérateur
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF TOLEDO MAIL STOP 942, TOLEDO, OHIO 43606-3390, United States
ISSN:
0030-8730
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=24755851
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24755851
Database:
PASCAL Archive

Further Information

A major goal in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane ℂ is to competely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. In [2007], the first author characterized the commutant of a Toeplitz operator T that has a quasihomogeneous symbol φ(r)eipθ with p > 0, in case it has a Toeplitz p-th root S with symbol ψ(r)eiθ: The commutant of T is the closure of the linear space generated by powers S that are Toeplitz. But the existence of a p-th root was known until now only when φ(r) = rm with m ≥ 0. Here we will show the existence of p-th roots for a much larger class of symbols, for example, those symbols for which where 0 < ai, bi for all 1 < i < k.