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Three Problems In Operator Theory And Complex Analysis, Cheng Chu
Three Problems In Operator Theory And Complex Analysis, Cheng Chu
Arts & Sciences Electronic Theses and Dissertations
This thesis concerns three distinct problems in operator theory and complex analysis. In Chapter 2, we study the following problem: On the Hardy space H^2, when is the product of a Hankel operator and a Toeplitz operator compact? We give necessary and sucient conditions for when such a product H_fT_g is compact. In Chapter 3, we discuss hyponormal Toeplitz operators. We show that for those operators, there exists a lower bound for the area of the spectrum. This extends the known estimate for the spectral area of Toeplitz operators with an analytic symbol. This part is joint work with Dmitry …