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Some invariant subspaces for subscalar operators

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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.

Abstract

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.

참고문헌 (31)

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