Spectral properties and restrictions of bounded linear operators. (English) Zbl 1312.47005

Summary: Assume that \(T\in L(X)\) is a bounded linear operator on a Banach space \(X\) and that \(T_n\) is a restriction of \(T\) on \(R(T^n)=T^n(X)\). In general, almost nothing can be said concerning the relationship between the spectral properties of \(T\) and \(T_n\). However, under some conditions, it is shown that several spectral properties introduced recently are the same for \(T\) and \(T_n\).


47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
47A53 (Semi-) Fredholm operators; index theories
47A55 Perturbation theory of linear operators
Full Text: DOI Euclid