Nonlinear Spectral Resolution

Abstract

A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems for certain possibly nonlinear operators which include bounded linear symmetric operators as special cases can be proved. The operational calculus of the classes of possibly nonlinear operators is developed and nonlinear spectral operators are given.