arXiv subjects

Carlos Kubrusly

Publications and source records attributed to Carlos Kubrusly.

5 recordsLinked to original sources

arXiv2026

Structural Properties and Normality Criteria for Subclasses of Normaloid Operators

We investigate structural properties and normality criteria for certain classes of bounded linear operators on a Hilbert space. We show that an operator $T$ with polar decomposition $T = U|T|$ is self-adjoint if and only if $T$ is absolute-$(p,r)$-paranormal and the partial isometry $U$ is self-adjoint. Extending Ando's Theorem, we prove that if $T$ is absolute-$(p,r)$-paranormal and $T^n$ is normal for some $n \in \mathbb{N}$, then $T$ itself is normal. We further show that if $T$ is absolute-$(p,r)$-paranormal and $T^2$ is compact, then $T$ is a compact normal operator. Finally, we obtain several characterizations of quasinormal partial isometries within the normaloid hierarchy.

math.FA↗

arXiv2026

Weak Quasistability and Rajchman measures

It is shown that weak quasistability does not imply power boundedness, but coercive power unbounded operators cannot be weakly quasistable.\ Although a finite measure over the unit disc is a Rajchman measure if and only if the position operator is weakly stable, it is shown that the position operator is weakly quasistable for every finite continuous measure over the unit disc.\ Corollaries linking Rajchman measures with weak stability and weak quasistability follow the above results.\

math.FA↗

arXiv2025

On roots of normal operators and extensions of Ando's Theorem

In this paper, we extend Ando's theorem on paranormal operators, which states that if $ T \in \mathfrak{B}(\mathcal{H}) $ is a paranormal operator and there exists $ n \in \mathbb{N} $ such that $ T^n $ is normal, then $ T $ is normal. We generalize this result to the broader classes of $ k $-paranormal operators and absolute-$ k $-paranormal operators. Furthermore, in the case of a separable Hilbert space $\mathcal{H}$, we show that if $ T \in \mathfrak{B}(\mathcal{H}) $ is a $ k $-quasi-paranormal operator for some $ k \in \mathbb{N} $, and there exists $ n \in \mathbb{N} $ such that $ T^n $ is normal, then $ T $ decomposes as $ T = T' \oplus T'' $, where $ T' $ is normal and $ T'' $ is nilpotent of nil-index at most $ \min\{n,k+1\} $, with either summand potentially absent.

math.FA↗

arXiv2024

Convergence of power sequences of operators via their stability

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power sequence if and only if it is a (not necessarily orthogonal) direct sum of an identity operator and a stable operator. This reduces the issue of convergence of the power sequence of an operator $T$ to the study of stability of $T$. The question of when the limit of the power sequence is an orthogonal projection is investigated. Among operators sharing this property are hyponormal and contractive ones. In particular, a hyponormal or a contractive operator with no identity part is stable if and only if its power sequence is convergent. In turn, a unitary operator has a weakly convergent power sequence if and only if its singular-continuous part is weakly stable and its singular-discrete part is the identity. Characterizations of the convergence of power sequences and stability of subnormal operators are given in terms of semispectral measures.

math.FA↗

arXiv2023

Closed-range posinormal operators and their products

We focus on two problems relating to the question of when the product of two posinormal operators is posinormal, giving (1) necessary conditions and sufficient conditions for posinormal operators to have closed range, and (2) sufficient conditions for the product of commuting closed-range posinormal operators to be posinormal with closed range. We also discuss the relationship between posinormal operators and EP operators (as well as hypo-EP operators), concluding with a new proof of the Hartwig-Katz Theorem, which characterizes when the product of posinormal operators on $\CC^n$ is posinormal.

math.FA↗