2024/09/04 by Dragoljub J. Kečkić, Kečkić, Dragoljub J., Zlatko Lazović +1
Mathematics · Physics and Astronomy · #47H08 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 46L08 #Secondary: 54E15
paper · pdf · doi:10.48550/arxiv.2409.02514
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a countably generated Hilbert C^*-module \mathcal M over a C^*-algebra \mathcal A. There is a measure of noncompactness λ defined, roughly as the distance from finitely generated projective submodules, which is independent of any topology. We compare λ to the Hausdorff measure of noncompactness with respect to the family of seminorms that induce a topology recently iontroduced by Troitsky, denoted by χ^*. We obtain λ≡χ^*. Related inequalities involving other known measures of noncompactness, e.g. Kuratowski and Istrăţescu are laso obtained as well as some related results on adjontable operators.