Hankel operators on the Segal -Bargmann space and symmetrically -normed ideals

Abstract

Consider the Hankel operators on the Segal-Bargmann space. Given any symbol function, we can consider the Hankel operator associated with it as well as the Hankel operator associated with the symbol function's complex conjugate. In this dissertation, we will give a necessary and sufficient condition for such a pair of Hankel operators to both be members of the symmetrically-normed ideal associated with a given symmetric norming function. This dissertation is a generalization of previous work done by J. Xia and D. Zheng, who obtained similar results for the particular case of the Schatten class ideals.