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arXiv · 2409.01167

A note on a Halmos problem

Maximiliano Contino·Eva Gallardo-Gutierrez
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Abstract

We address the existence of non-trivial closed invariant subspaces of operators $T$ on Banach spaces whenever their square $T^2$ have or, more generally, whether there exists a polynomial $p$ with $\mbox{deg}(p)\geq 2$ such that the lattice of invariant subspaces of $p(T)$ is non-trivial. In the Hilbert space setting, the $T^2$-problem was posed by Halmos in the seventies and in 2007, Foias, Jung, Ko and Pearcy conjectured it could be equivalent to the \emph{Invariant Subspace Problem}.

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Maximiliano Contino, Eva Gallardo-Gutierrez. 2024-09-02. A note on a Halmos problem. https://arxiv.org/abs/2409.01167

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