How to generalize the concept of eigenvalues of quadratic forms to eigenvalues of arbitrary, even, homogeneous continuous functionals, if stability of the set of eigenvalues under small perturbations is required? We compare two possible generalizations, Gromov's homotopy significant spectrum and the Krasnoselskii spectrum. We show that the Krasnoselskii spectrum is contained in the homotopy significant spectrum, but provide a counterexample to the opposite inclusion. Moreover, we propose a small modification of the definition of the homotopy significant spectrum for which we can prove stability.

中文翻译：

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与 Krasnoselskii 谱相比的同伦显着谱

如果需要小扰动下特征值集的稳定性，如何将二次型特征值的概念推广到任意、均匀、齐次连续泛函的特征值？我们比较了两种可能的概括，Gromov 的同伦显着谱和 Krasnoselskii 谱。我们表明 Krasnoselskii 谱包含在同伦显着谱中，但为相反的包含提供了一个反例。此外，我们建议对同伦显着谱的定义进行小的修改，我们可以证明其稳定性。