Linear independence, equivalence and minimality of root vectors for certain nonlinear spectral problems (Q757802)

Linear independence, equivalence and minimality of root vectors of operator-functions of the form \[ L=\sum_{r}\lambda^ rL_{0,r}+\sum_{q}\sum_{r}(\lambda -\alpha_ q)^{- r}L_{qr}+S(\lambda) \] are considered. Here \(L_{qr}\) are bounded operators over a Hilbert space H and S(\(\lambda\)) is a weakly continuous operator function.