Hyponormality of Toeplitz operators and composition operators
Abstract
A Hilbert space operator T is hyponormal if $T*T-TT*$ is positive. In chapter one we consider hyponormality of Toeplitz operators on the Bergman space with a symbol in the class of functions $f+\overline{g},$ where f and g are bounded and analytic in the unit disk. Under a smoothness assumption, we give a necessary condition. We give a sufficient condition in the case f is a monomial and g is a polynomial. In chapter two we study the hyponormality of the adjoints of composition operators, on the Hardy space, with a linear fractional symbol. We give a necessary condition and find an equivalent condition to hyponormality. Using the mentioned equivalent condition we show hyponormality in a special case.
Degree
Ph.D.
Advisors
Cowen, Purdue University.
Subject Area
Mathematics
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