Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA : L(H) -L(H) X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L(2-H H), and gave a g6neralisation of Stampflli theorem.展开更多
文摘Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA : L(H) -L(H) X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L(2-H H), and gave a g6neralisation of Stampflli theorem.