M. Aouichaoui

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math.FA2026

Solutions to some open problems in matrix analysis

Mohamed Amine Aouichaoui, Eun-Young Lee

We solve a problem posed by Audenaert and Kittaneh in 2012 by proving that the Aujla--Bourin subadditivity inequality can be strengthened to an optimal form. We also answer questio…

math.FA2026

A proof of the Fong--Tsui conjecture

Mohamed Amine Aouichaoui, Fuad Kittaneh, Yicen Ma

We prove that a bounded operator $T$ on a complex Hilbert space is self-adjoint whenever $|T|\leq|\re T|$, as conjectured by Fong and Tsui \cite{FT}.

math.FA2026

Sharp spectral constants for scaled $q$ -numerical ranges

Mohamed Amine Aouichaoui, Ryan O'Loughlin

For $n \geq 2$ , $A \in M_{n} (C)$ and $0 < ∣ q ∣ \leq 1$ , let $Ω_{q} (A) = q^{- 1} W_{q} (A)$ be the scaled $q$ -numerical range. We prove that for every $γ \geq 1$ , \[ Ω_{η(γ)}(A) =\bigcup_{κ…

math.FA2026

On $m$ -partial isometries: spectra, weighted shifts, and similarity

Mohamed Amine Aouichaoui, Michał Buchała, Stephan Ramon Garcia

The aim of this paper is to study $m$ -partial isometries on Hilbert spaces, a natural extension of partial isometries and $m$ -isometries. We establish structural and spectral resul…

Solutions to some open problems in matrix analysis

A proof of the Fong--Tsui conjecture

Sharp spectral constants for scaled q-numerical ranges

On m-partial isometries: spectra, weighted shifts, and similarity

Sharp spectral constants for scaled $q$ -numerical ranges

On $m$ -partial isometries: spectra, weighted shifts, and similarity