Many parameter Hoelder perturbation of unbounded operators

If $u\mapsto A(u)$ is a $C^{0,α}$-mapping, for $0< α\le 1$, 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 $C^{0,α}$ in $u$.

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