, Volume 353, Issue 2, pp 519-522
Date: 29 Jun 2011

Many parameter Hölder perturbation of unbounded operators

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Abstract

If \({u \mapsto A(u)}\) is a C 0,α -mapping, for 0 < α ≤ 1, having as values unbounded self-adjoint operators with compact resolvents and common domain of definition, parameterized by u in an (even infinite dimensional) space, then any continuous (in u) arrangement of the eigenvalues of A(u) is indeed C 0,α in u.