Many parameter Hölder perturbation of unbounded operators (Q425141)

The perturbation theory for linear operators was motivated by the study of eigenvalues for Schrödinger operators, with pioneering works due to Rellich and Kato. Continuing the previous work [``Differentiable perturbation of unbounded operators'', Math. Ann. 327, No. 1, 191--201 (2003; Zbl 1054.47014)] of the first two authors of this paper, the authors prove here that, if \(u\mapsto A(u)\) is a \(C^{0,\alpha}\) unbounded selfadjoint operator-valued mapping, \(0<\alpha\leq 1\), with compact resolvent and common domain, then any continuous (in \(u\)) arrangement of the eigenvalues of \(A(u)\) is \(C^{0,\alpha}\) in \(u\).