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

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Veröffentlicht in:Taehan Suhakhoe hoebo 2011, Vol.48 (6), p.1129-1135
1. Verfasser: Yoo, Jong-Kwang
Format: Artikel
Sprache:kor
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Zusammenfassung: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.
ISSN:1015-8634