Abstract
Let $X$ be an infinite dimensional complex vector space. We show that a non-constant endomorphism of $X$ has a proper hyperinvariant subspace if and only if its spectrum is non-void. As an application we show that each non-constant continuous endomorphism of the locally convex space $(s)$ of all complex sequences has a proper closed hyperinvariant subspace.
Citation
Wieslaw Zelazko. "On existence of hyperinvariant subspaces for linear maps." Banach J. Math. Anal. 3 (1) 143 - 148, 2009. https://doi.org/10.15352/bjma/1240336431
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