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A Class of m-Complex Symmetric Operators on Hardy Space
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In this paper,we study the necessary and sufficient condition that the Toeplitz operators with respect to the conjugations of one permutation are 2-complex symmetric.Firstly,we introduce a class of conjugations called the conjugations of one permutations on the classical Hardy space.Secondly,Toeplitz operators are completely characterized as 2-complex symmetric structure under this class of conjugations.The matrix representation of Toeplitz operators in the classical regular orthogonal basis on Hardy space is used to describe this class of 2-complex symmetric Toeplitz operators.Finally,we add two preconditions fn=-f-n and fn=f-n respectively to the Toeplitz operators,and we get more simplified results.Under the second condition,we study the 3-complex symmetry of Toeplitz operators,and we get the same result for Tf is a 3-CSO with the conjugation C(i,j)and 2-CSO's.
m-complex symmetric operatorToeplitz operatorHardy space
Jia FU、Xinmei LI、Ran LI
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School of Mathematics,Liaoning Normal University,Liaoning 116029,P.R.China
国家自然科学基金Educational Foundation of Liaoning Province
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