Complex symmetry of Toeplitz operators on Hardy spaces
Complex symmetric operators are abstracts from the concept of complex symmetric matrices.In this paper,we study how to characterize a class of complex symmetric Toeplitz operators on classical Hardy Spaces through matrix.Firstly,two new classes of conju-gations are defined on Hardy spaces,which are n-inverted conjugations and n-quadratic inverted conjugations respectively.Secondly,it is described that the Toeplitz operator is complex symmetric under conjugations in odd and even cases,and the necessary and sufficient conditions for Toeplitz operator to be complex symmetric under conjugations on Hardy spaces are given by using the matrix representa-tion of the Toeplitz operator under classical orthogonal basis respectively.Finally,this paper summarizes and looks forward to the prob-lem of whether Toeplitz operator can be described as m-complex symmetric relative to this class of conjugations.
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