Banach Journal of Mathematical Analysis

On existence of hyperinvariant subspaces for linear maps

Wieslaw Zelazko

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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.

Article information

Source
Banach J. Math. Anal. Volume 3, Number 1 (2009), 143-148.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336431

Digital Object Identifier
doi:10.15352/bjma/1240336431

Mathematical Reviews number (MathSciNet)
MR2461754

Zentralblatt MATH identifier
1171.47004

Subjects
Primary: 47A15: Invariant subspaces [See also 47A46]
Secondary: 15A04: Linear transformations, semilinear transformations

Keywords
hyperinvariant subspace locally convex space endomorphism

Citation

Zelazko, Wieslaw. On existence of hyperinvariant subspaces for linear maps. Banach J. Math. Anal. 3 (2009), no. 1, 143--148. doi:10.15352/bjma/1240336431. https://projecteuclid.org/euclid.bjma/1240336431


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References

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