Some invariant subspaces for subscalar operators
Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1129-1135
https://doi.org/10.4134/BKMS.2011.48.6.1129
Published online November 1, 2011
Jong-Kwang Yoo
Chodang University
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 $(\delta)$ on a Banach space of dimension greater than 1 has a non-trivial invariant closed linear subspace.
Keywords : algebraic spectral subspace, analytic spectral subspace, decomposable operator, invariant subspaces property $(\beta)$, property $(\delta),$ subscalar operator
MSC numbers : Primary 47A11, 47A53
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