SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS

Title & Authors
SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS
Yoo, Jong-Kwang;

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 ($\small{{\delta}}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.
Keywords
algebraic spectral subspace;analytic spectral subspace;decomposable operator;invariant subspaces property ($\small{{\beta}}$);property ($\small{{\delta}}$);subscalar operator;
Language
English
Cited by
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