# SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS

• Yoo, Jong-Kwang (Department of Liberal Arts and Science Chodang University)
• Published : 2011.11.30

#### Abstract

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 (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

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