2022/05/18 by Laurent W. Marcoux, Heydar Radjavi, Marcoux, Laurent W. +3
Mathematics · #47A58 #47B47 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2205.09043
openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the norm-closures of the set \mathfrakC_\mathfrakE of commutators of idempotent operators and the set \mathfrakE - \mathfrakE of differences of idempotent operators acting on a finite-dimensional complex Hilbert space, as well as characterising the intersection of the closures of these sets with the set K(H) of compact operators acting on an infinite-dimensional, separable Hilbert space. Finally, we characterise the closures of the set \mathfrakC_\mathfrakP of commutators of orthogonal projections and the set \mathfrakP - \mathfrakP of differences of orthogonal projections acting on an arbitrary complex Hilbert space.