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 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 non-trivial invariant closed lin...

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Veröffentlicht in:Taehan Suhakhoe hoebo 2011, 48(6), , pp.1129-1135
1. Verfasser: Yoo, Jong-Kwang
Format: Artikel
Sprache:eng
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수학
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Zusammenfassung: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 non-trivial invariant closed linear subspace. KCI Citation Count: 1
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.2011.48.6.1129