On existence of hyperinvariant subspaces for linear maps
Wieslaw Zelazko
Source: Banach J. Math. Anal.
Volume 3, Number 1
(2009), 143-148.
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.
Primary Subjects: 47A15
Secondary Subjects: 15A04
Keywords: hyperinvariant subspace; locally convex space; endomorphism
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336431
Mathematical Reviews number (MathSciNet):
MR2461754
Zentralblatt MATH identifier:
05379957
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Mathematical Reviews (MathSciNet):
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W. Żelazko, Operators on locally convex spaces, in Operator Theory: Advances and Applications vol. 187, 237--247, 2008 Birkhauser Verlag Basel.
