Left Weyl Research Articles

Right and Left Weyl Operator Matrices in a Banach Space Setting

LetXi,Yii=1,2be Banach spaces. The operator matrix of the formMC=AC0Bacting betweenX1⊕X2andY1⊕Y2is investigated. By using row and column operators, equivalent conditions are obtained forMCto be left Weyl, right Weyl, and Weyl for someC∈ℬX2,Y1, respectively. Based on these results, some sufficient conditions are also presented. As applications, some discussions on Hamiltonian operators are given in the context of Hilbert spaces.

Weylness of 2 × 2 operator matrices

AbstractLet and be complex separable infinite‐dimensional Hilbert spaces. Given the operators and , we define where is an unknown element. In this paper, a necessary and sufficient condition is given for to be a right Weyl (left Weyl, or Weyl) operator for some . Moreover, some relevant properties and illustrating examples are also given.