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 Some invariant subspaces for subscalar operators Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1129-1135 https://doi.org/10.4134/BKMS.2011.48.6.1129Printed 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 Downloads: Full-text PDF