Many parameter Hoelder perturbation of unbounded operators

Andreas Kriegl, Peter W. Michor, Armin Rainer

Published 2006-11-16, updated 2009-06-08Version 2

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