The Studies On Several Kinds Of Symmetric Opetrtors

In this paper,we mainly investigate some local spectral properties of rm-skew complex symmetric operators,(m,C)-isometric operators.When T is a complex symmetric oper-ators,We investigate some properties of binormal operators.we solve the problem that binormal is not closed under an additional condition.We prove that T is a binormal oper-ator,if and only if C commutes with TT*T*T,if T ?L(H)be a skew complex symmetric operator.The main contents are as follows.First,some backgrounds and current situations of complex symmetric operators,(m,C)-isometric operators and binormal complex symmetric operators are given,and some basic conceptions which will be used in this paper are listed.Second,we investigate some local spectral properties of m-skew complex symmetric operators and give some local spectral properties of the operator T + N after adding the nilpotent disturbance operator N to the m-skew symmetric operator T.Third,we give some spectral properties and spectral relations of(m,C)-isometric operators and give some local spectral properties of the operator T + N and T + A after adding a nilpotent disturbance operator N and a algebraic operator A to the m-skew symmetric operator T.Last,if the operator T is a complex symmetry operator,we give the condition that the binormal operator and the n-binormal operator become normal operators and n-normal operator.We solve the problem that binormal is not closed under addition.We also proved that if T is skew symmetric operators,the operator T is binormal operator if and only if C commutes with TT*T*T.