Abstract
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.
基金项目
国家自然科学基金(11901269)
Educational Foundation of Liaoning Province(JYTMS20231041)
NETL
NSTL
万方数据