João R. Carmo

activity

20192026

collaborators

7 papers

math.FA2026

Minimality of $T_{z}^{*}$ -Invariant Subspaces of $H^{2} (D^{2})$

João Marcos R. do Carmo, Marcos S. Ferreira

In this paper, we establish necessary conditions for the minimality of infinite-dimensional $T_{z}^{*}$ -invariant subspaces of $H^{2} (D^{2})$ . More precisely, we prove that if $M\s…

math.FA2026

Universal operators: topology and consequences of ISP failure

João Carmo, Ben-Hur Eidt, Waleed Noor

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-dimens…

math.FA2026

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

Marcos dos Santos Ferreira, João Marcos Ribeiro do Carmo

We study the rigidity of the orthogonal projections $P_{n} : H^{2} (D^{2}) \to H_{n}$ , where $H^{2} (D^{2}) = ⨁_{n = 0}^{\infty} H_{n}$ and each $H_{n}=H^{2}(z)…

math.FA2026

Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk

Carlos F. Álvarez, João R. Carmo, Juan Manzur

We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w, φ}$ on Banach spaces of analytic functions on the unit disk $D$ . Under natural conditi…

math.FA2023

On the invariant subspace problem via universal Toeplitz operators on the Hardy space $H^{2} (D^{2})$

João Marcos R. do Carmo, Marcos S. Ferreira

The Invariant Subspace Problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operato…

math.FA2023

Minimal invariant subspaces for an affine composition operator

João R. Carmo, Ben Hur Eidt, S. Waleed Noor

The composition operator $C_{ϕ_{a}} f = f \circ ϕ_{a}$ on the Hardy-Hilbert space $H^{2} (D)$ with affine symbol $ϕ_{a} (z) = a z + 1 - a$ and $0 < a < 1$ has the property that the Invariant Subspa…

math.FA2019

Universal composition operators

João R. Carmo, S. Waleed Noor

A Hilbert space operator $U$ is called universal (in the sense of Rota) if every Hilbert space operator is similar to a multiple of $U$ restricted to one of its invariant subspaces…

Minimality of Tz∗​-Invariant Subspaces of H2(D2)

Universal operators: topology and consequences of ISP failure

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

Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk

On the invariant subspace problem via universal Toeplitz operators on the Hardy space H2(D2)

Minimal invariant subspaces for an affine composition operator

Universal composition operators

Minimality of $T_{z}^{*}$ -Invariant Subspaces of $H^{2} (D^{2})$

On the invariant subspace problem via universal Toeplitz operators on the Hardy space $H^{2} (D^{2})$