Bases from eigensubspaces of a nondissipative operator and the characteristic function
Let L be a bounded operator in a Hilbert space such that Im L is a trace class operator. Let \(E_{\lambda_ n}\) be the family of eigenspaces of L corresponding to the eigenvalues \(\lambda_ n\) \((n=1,2,...)\). The completeness of \(\{E_{\lambda_ n}\}\) is assumed. Necessary and sufficient conditions are given for the uniform minimality of \(\{E_{\lambda_ n}\}\) and the validity of the following assertion: \(E_{\lambda_ n}\) is a Riesz base.
scientific article; zbMATH DE number 4132951