Lipschitz-α算子的M-谱理论

M-Spectral Theory of Lipschitz-α Operators

本文运用一个选定的可逆Lip-α算子M作为尺度算子(称为谱尺度),引入两个Banach空间之间的非线性Lip-α算子的M-豫解集、M-谱集、M-谱半径、豫解集、谱集及谱半径,证明了它们的一列系重要性质,给出了M-谱的一个摄动定理,初步建立了Lip-α算子的M-谱理论,使得现有的谱理论成为其特例.

Using a selected invertible Lip-a operator M as the scale operator called the spectral scale, we introduce the M-resolvent set, M-spectrum, M-spectral radius, resolvent set, spectrum and spectral radius for a nonlinear Lipschitz-α operator between two Banach spaces. A number of important properties on them are proved. We also establish a spectral perturbation theorem for Lip-a operators. These results give rise to the elementary theory of M-spectra and generalize the usual spectral theory.