On quasinormal,subnormal, and hyponormal Toeplitz operators |
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Authors: | Nazih Faour |
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Institution: | 1. Mathematics Department, Kuwart University, P.O. Box 5969, 13060, Safat, Kuwait
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Abstract: | Let ? be a non-constant function inL ∞(D) such thatφ=φ 1+φ 2, whereφ 1 is an element in the Bergman spaceL a 2 (D), and \(\phi _2 \in \overline {L_a^2 (D)} \) , the space of all complex conjugates of functions inL a 2 (D). In this paper, it is shown that if 1 is an element in the closure of the range of the self-commutator ofT ?, \(T_{\bar \phi } T_\phi - T_\phi T\phi \) , then the Toeplitz operatorT ? defined ofL a 2 (D) is not quasinormal. Moreover, if \(\phi = \psi + \lambda \bar \psi \) , whereψ∈ H ∞(D), and λεC, it is proved that ifT ? is quasinormal, thenT ? is normal. Also, the spectrum of a class of pure hyponormal Toeplitz operators is determined. |
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