Toeplitz operators and hyponormality
Abstract
We consider Toeplitz operators on three spaces of analytic functions: the Hardy space, the Bergman space, and the space H 2(μ) for a special choice of measure μ. An operator A is hyponormal if its self-commutator A* A − AA* is positive. In the first chapter we give a generalization of a result of Sadraoui involving the derivatives of the analytic and anti-analytic parts of the symbol of certain Toeplitz operators. A condition equivalent to hyponormality of an operator A is that the norm of Ax be greater than or equal to the norm of A*x for all vectors x. In the second chapter we present a result concerning the set of vectors for which equality holds when the operator belongs to a certain class of hyponormal Toeplitz operators on the Hardy space. In the third chapter we give a condition that is useful when investigating whether certain Bergman space Toeplitz operators are hyponormal. We present several results about Toeplitz operators on the space H2(μ) in the fourth chapter, including some that involve the relationship with hyponormality of the corresponding Toeplitz operators on the Hardy space.
Degree
Ph.D.
Advisors
Cowen, Purdue University.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.