Abstract
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.
Highlights
By using row and column operators, equivalent conditions are obtained for MC to be left Weyl, right Weyl, and Weyl for some C ∈ B(X2, Y1), respectively
Some discussions on Hamiltonian operators are given in the context of Hilbert spaces
Most of these papers worked in the context of Hilbert spaces, some results on the invertibility and Fredholm theory were established in Banach spaces [5,6,7]
Summary
E sets of all left and right Fredholm operators are, respectively, defined as En, there exists C ∈ B(X2, Y1) such that MC is Weyl if and only if A is left Fredholm, B is right Since A S is right Fredholm, β(Δ) β A S < ∞, and R(Δ) is clearly complemented in the left implies that α(Δ)
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