Douglas factorization theorem revisited

DOI10.1090/proc/14757zbMath1462.47012arXiv1807.00579OpenAlexW3103526290WikidataQ127496186 ScholiaQ127496186MaRDI QIDQ5212418

Qingxiang Xu, Vladimir M. Manuilov, Mohammad Sal Moslehian

Publication date: 29 January 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00579

zbMATH Keywords

operator equationHilbert \(C^\ast\)-moduleregular operatorsemi-regular operator

Mathematics Subject Classification ID

(C^*)-modules (46L08) Equations involving linear operators, with operator unknowns (47A62) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items

Products of projections, polar decompositions and norms of differences of two projections ⋮ Some \(\mathbb{A}\)-numerical radius inequalities for \(d\times d\) operator matrices ⋮ On 𝔸-numerical radius inequalities for 2 × 2 operator matrices ⋮ On m-quasi-totally-(α,β)-normal operators ⋮ Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators ⋮ Solvability of the system of operator equations \(AX=C, XB=D\) in Hilbert \(C{{}^*}\)-modules ⋮ Certain properties of orthogonal projections ⋮ Generalized parallel sum of adjointable operators on Hilbert C*-modules ⋮ Harmonious projections and Halmos' two projections theorem for Hilbert \(C^\ast \)-module operators ⋮ Pedersen-Takesaki operator equation and operator equation \(AX = B\) in Hilbert \(C^*\)-modules ⋮ \(C^*\)-isomorphisms associated with two projections on a Hilbert \(C^*\)-module ⋮ The polar decomposition of the product of three operators ⋮ The Douglas lemma for von Neumann algebras and some applications ⋮ On \(\mathbb{A}\)-numerical radius equalities and inequalities for certain operator matrices ⋮ Vector-valued reproducing kernel Hilbert \(C^*\)-modules ⋮ Maps preserving the Douglas solution of operator equations ⋮ Spectral analysis of bounded operators on semi-Hilbertian spaces

Cites Work

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• Factorizations of linear relations
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• The solutions to some operator equations with corresponding operators not necessarily having closed ranges
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• The $C^*$-algebra generated by two projections.

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