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arXiv · 1511.07771

Hyperinvariant subspaces of locally nilpotent linear transformations

Pudji Astuti·Harald K. Wimmer
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Abstract

A subspace $X$ of a vector space over a field $K$ is hyperinvariant with respect to an endomorphism $f$ of $V$ if it is invariant for all endomorphisms of $V$ that commute with $f$. We assume that $f$ is locally nilpotent, that is, every $ x \in V $ is annihilated by some power of $f$, and that $V$ is an infinite direct sum of $f$-cyclic subspaces. In this note we describe the lattice of hyperinvariant subspaces of $V$. We extend results of Fillmore, Herrero and Longstaff (Linear Algebra Appl. 17 (1977), 125--132) to infinite dimensional spaces.

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Pudji Astuti, Harald K. Wimmer. 2015-10-26. Hyperinvariant subspaces of locally nilpotent linear transformations. https://arxiv.org/abs/1511.07771

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