6 papers
A Grassmann formula for the spectral order of matrices
Mohamed Amine Aouichaoui, Eun-Young Lee
For Hermitian matrices and , we prove that $(A\join B)\oplus(A\meet B)$ is unitarily equivalent to , where the join and meet are taken in Olson's spectral order.…
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…
A proof of the Fong--Tsui conjecture
Mohamed Amine Aouichaoui, Fuad Kittaneh, Yicen Ma
We prove that a bounded operator on a complex Hilbert space is self-adjoint whenever $|T|\leq|\re T|$, as conjectured by Fong and Tsui \cite{FT}.
Sharp spectral constants for scaled -numerical ranges
Mohamed Amine Aouichaoui, Ryan O'Loughlin
For , and , let be the scaled -numerical range. We prove that for every , \[ Ω_{η(γ)}(A) =\bigcup_{κ…
On -partial isometries: spectra, weighted shifts, and similarity
Mohamed Amine Aouichaoui, Michał Buchała, Stephan Ramon Garcia
The aim of this paper is to study -partial isometries on Hilbert spaces, a natural extension of partial isometries and -isometries. We establish structural and spectral resul…
The square root theorem for positive semidefinite matrices and their monotonicity
Mohamed Amine Aouichaoui, Mohammed Hichem Mortad
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.