Quasicontinuous functions on the unit circle and Toeplitz operators in symmetric normed ideals
Orenstein, Adam Seth
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In this dissertation, we will solve two problems. First we will give a complete description of I, the set of invertible quasicontinuous functions on the unit circle. After doing this, we will then classify the path-connected components of I and show that I has uncountably many path-connected components. We will then use the above classifications to characterize F, the set of Fredholm operators of the C*-algebra generated by the Toeplitz operators T &phgr; with quasicontinuous symbols &phgr;. Then we will classify the path-connected components of F and show that F also has uncountably many path-connected components. Second, we will give necessary and sufficient conditions for a Toeplitz operator T &ngr; , having a positive Borel measure &ngr; for a symbol, on the Fock Space (also known as the Segal-Bargmann space) to be in the symmetrically-normed ideal C &PHgr; for an arbitrary symmetric norming function &PHgr;.