SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS

Jong-Kwang Yoo
2011 Bulletin of the Korean Mathematical Society  
In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscalar operator is nilpotent. We also prove that every subscalar operator with property (δ) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.
doi:10.4134/bkms.2011.48.6.1129 fatcat:dequzzkwczcuzakrvm6cxkukpy