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Indexed by:期刊论文
Date of Publication:2009-09-01
Journal:INTEGRAL EQUATIONS AND OPERATOR THEORY
Included Journals:SCIE、Scopus
Volume:65
Issue:1
Page Number:115-129
ISSN No.:0378-620X
Key Words:Hyponormality; weighted Bergman space; Hankel operator; Toeplitz operator
Abstract:Consider phi - f + (g) over bar, where f and g are polynomials, and let T(phi) be the Toeplitz operators with the symbol phi. It is known that if T(phi) is hyponormal then vertical bar f'(z)broken vertical bar(2) >= vertical bar g'(z)vertical bar(2) on the unit circle in the complex plane. In this paper, we show that it is also a necessary and sufficient condition under certain assumptions. Furthermore, we present some necessary conditions for the hyponormality of T(phi) on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee.