Author

João R. Carmo

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Preprint Oct 2026

Minimality of $T_z^*$-Invariant Subspaces of $H^2(\mathbb D^2)$

In this paper, we establish necessary conditions for the minimality of infinite-dimensional $T_z^*$-invariant subspaces of $H^2(\mathbb D^2)$. More precisely, we prove that if $M\subset H^2(\mathbb D^2)$ is an infinite-dimensional, minimal $T_z^*$-invariant subspace, then, for every $n\in\mathbb N_0$, either $\overline...

João R. Carmo, Marcos R. S. Ferreira · 0 citations

Preprint Oct 2026

Universal operators: topology and consequences of ISP failure

Assuming a negative answer to the invariant subspace problem for separable complex Hilbert spaces, we prove that every universal operator has a continuum of minimal infinite-dimensional invariant subspaces with pairwise trivial intersections. These subspaces can be chosen so that the restrictions are invertible and the...

João R. Carmo, B. Eidt, Waleed Noor · 0 citations

Preprint Sep 2026

Projections and minimal invariant subspaces in the Hardy space over the bidisk

We study the rigidity of the orthogonal projections $P_{n}:H^2(\mathbb{D}^2)\rightarrow H_{n}$, where $H^{2}(\mathbb{D}^{2})=\bigoplus_{n=0}^{\infty}H_{n}$ and each $H_{n}=H^{2}(z)w^{n}$ is a reducing subspace for $T_{z}$, and we derive properties of the minimal invariant subspaces of $T_{z}^{*}$. Our main result estab...

Marcos S. Ferreira, João R. Carmo · 1 citation