Products of Toeplitz operators on the Fock space

Let f and g be functions, not identically zero, in the Fock space $F^{2}_{\alpha}$ of ℂ n . We show that the product T f T g̅ of Toeplitz operators on $F^{2}_{\alpha}$ is bounded if and only if f(z) = e q(z) and g(z) = ce −q(z) , where c is a nonzero constant and q is a linear polynomial.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-07, Vol.142 (7), p.2483-2489
Main Authors: CHO, HONG RAE, PARK, JONG-DO, ZHU, KEHE
Format: Article
Language:English
Subjects:
Degrees of polynomials
Entire functions
Factorization
Kernel functions
Linear polynomials
Mathematical functions
Polynomials
Unit ball
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Summary:Let f and g be functions, not identically zero, in the Fock space $F^{2}_{\alpha}$ of ℂ n . We show that the product T f T g̅ of Toeplitz operators on $F^{2}_{\alpha}$ is bounded if and only if f(z) = e q(z) and g(z) = ce −q(z) , where c is a nonzero constant and q is a linear polynomial.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2014-12110-1