A. Kriegl, P.W. Michor
Differentiable Perturbation of Unbounded Operators
The paper is published: Math. Ann. 327 (2003) 191-201

MSC:

47A55 Perturbation theory

47A75 Eigenvalue problems, See also {49Rxx}

Abstract: If $A(t)$ is a $C^{1,\al}$-curve of unbounded self-adjoint
operators on Hilbert space with compact resolvents and common domain
of definition, then the eigenvalues can be chosen $C^1$ in $t$.
Keywords: perturbation theory, differentiable choice of eigenvalues