Harmonious projections and Halmos' two projections theorem for Hilbert \(C^\ast \)-module operators

DOI10.1016/j.laa.2020.05.012zbMath1444.46038OpenAlexW3027631439MaRDI QIDQ2187394

Qingxiang Xu, Guanjie Yan

Publication date: 2 June 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2020.05.012

zbMATH Keywords

orthogonal complementHalmos' two projections theoremharmonious projectionHilbert \(C^\ast \)-module

Mathematics Subject Classification ID

(C^*)-modules (46L08) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (4)

Characterizations of the harmonious pairs of projections on a Hilbert C*-module ⋮ \(C^*\)-isomorphisms associated with two projections on a Hilbert \(C^*\)-module ⋮ Norm inequalities associated with two projections ⋮ The Frobenius distances from projections to an idempotent matrix

Cites Work

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• Products of orthogonal projections and polar decompositions
• A gentle guide to the basics of two projections theory
• On pairs of projections in a Hilbert space
• Closed range and nonclosed range adjointable operators on Hilbert \(C^*\)-modules
• Geometric significance of Toeplitz kernels
• The polar decomposition for adjointable operators on Hilbert \(C^*\)-modules and centered operators
• Halmos' two projections theorem for Hilbert \(C^\ast\)-module operators and the Friedrichs angle of two closed submodules
• The numerical range of a pair of projections
• Sharp Norm-Estimations for Moore–Penrose Inverses of Stable Perturbations of Hilbert $C^*$-Module Operators
• Douglas factorization theorem revisited
• Two Subspaces

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