Densely Defined Closed On The Circumference Of Toeplitz Operators,

In this paper, the Toeplitz operators with symbols in L2(T) are defined, and they are proved to be densely defined and closed. The conditions for their range to be closed are given. Finally the resolvent convergence of Toeplitz operator sequence is discussed, and sufficient conditions of resolvent convergence in norm and resolvent convergence in strong operator topology are given.