Many parameter Hoelder perturbation of unbounded operators

Abstract

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 $u$.

LaTeX, 4 pages; The result is generalized from Lipschitz to Hoelder. Title changed

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