Pedersen-Takesaki operator equation and operator equation \(AX = B\) in Hilbert \(C^*\)-modules

DOI10.1016/j.jmaa.2022.126878OpenAlexW4309825754MaRDI QIDQ2682679

Rasoul Eskandari, Xiao Chun Fang, Mohammad Sal Moslehian, Qingxiang Xu

Publication date: 1 February 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.12601

zbMATH Keywords

positive solutionoperator equationHilbert \(C^*\)-moduleDouglas lemma

Mathematics Subject Classification ID

(C^*)-modules (46L08) Special classes of linear operators (47Bxx) General theory of linear operators (47Axx)

Related Items (2)

On the solution of nonlinear operator equations and the invariant subspace ⋮ Characterizations of generalized pencils of pairs of projections

Cites Work

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• Furuta type inequalities dealing with Pedersen-Takesaki type operator equations
• Operator equations \(AX+YB=C\) and \(AXA^\ast + BYB^\ast =C\) in Hilbert \(C^\ast\)-modules
• Solutions to operator equations on Hilbert \(C^*\)-modules. II
• The operator equation \(T(H^{1/n}T)^ n=K\)
• Closed range and nonclosed range adjointable operators on Hilbert \(C^*\)-modules
• Douglas' + Sebestyén's lemmas = a tool for solving an operator equation problem
• Positive semi-definite matrices of adjointable operators on Hilbert \(C^{*}\)-modules
• The operator equation \(K^p = H^{\frac \delta 2}T^{\frac 1 2}(T^{\frac 1 2}H^{\delta +r}T^{\frac 1 2})^{\frac {p-\delta}{\delta +r}}T^{\frac 1 2}H^{\frac \delta 2}\) and its applications
• The Radon-Nikodym theorem for von Neumann algebras
• Solvability of the system of operator equations \(AX=C, XB=D\) in Hilbert \(C{{}^*}\)-modules
• Douglas factorization theorem revisited
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
• Inner Product Modules Over B ∗ -Algebras
• Shorter Notes: The Operator Equation THT = K
• Theory of operator algebras I.

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