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Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkoff-Kellogg theorem

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  • It is well known that any (nontrivial) linear compact self-adjoint operator acting in a Hilbert space possesses at least one non-zero eigenvalue. We present a generalization of this to nonlinear mappings as in the title, and discuss the relations of our results with the Birkhoff-Kellogg Theorem on one side, and with the spectral properties of self-adjoint operators on the other.
    Mathematics Subject Classification: Primary: 47J10; Secondary: 47J10.


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