SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS
SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS
In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (<TEX>${\delta}$</TEX>) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.