Solutions to operator equations on Hilbert \(C^*\)-modules

DOI10.1016/j.laa.2009.07.009zbMath1175.47014OpenAlexW2032389887MaRDI QIDQ734928

Jing Yu, Xiao Chun Fang, Hong Liang Yao

Publication date: 14 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.07.009

zbMATH Keywords

solutionpositive solutionHilbert \(C^{*}\)-moduleHermitian solution

Mathematics Subject Classification ID

(C^*)-modules (46L08) Equations involving linear operators, with operator unknowns (47A62)

Related Items (27)

The \(\{P, Q, k + 1 \}\)-reflexive solution to system of matrix equations \(A X = C\), \(X B = D\) ⋮ Solvability of the system of operator equations \(AX=C, XB=D\) in Hilbert \(C{{}^*}\)-modules ⋮ Closed range and nonclosed range adjointable operators on Hilbert \(C^*\)-modules ⋮ Solutions to operator equations on Hilbert \(C^*\)-modules. II ⋮ On \(K\)-woven frames in Hilbert \(C^\ast\)-modules ⋮ Compatibility and Schur complements of operators on Hilbert \(C^*\)-module ⋮ On the Hermitian \(R\)-conjugate solution of a system of matrix equations ⋮ On the Hermitian solutions to a system of adjointable operator equations ⋮ Parallel sum of positive adjointable operators on Hilbert \(C^{*}\)-modules ⋮ Fusion frames for operators in Hilbert \(C^\ast\)-modules ⋮ G-frames for operators in Hilbert $C^{\ast}$-modules ⋮ Variational inequalities with multivalued lower order terms and convex functionals in Orlicz-Sobolev spaces ⋮ Unnamed Item ⋮ Operator equations \(AX+YB=C\) and \(AXA^\ast + BYB^\ast =C\) in Hilbert \(C^\ast\)-modules ⋮ Existence results for some nonlinear elliptic equations with measure data in Orlicz-Sobolev spaces ⋮ The common positive solution to adjointable operator equations with an application ⋮ On majorization and range inclusion of operators on Hilbert C*-modules ⋮ Common nonnegative definite solutions of some classical matrix equations ⋮ Positive solutions to a system of adjointable operator equations over Hilbert \(C^*\)-modules ⋮ A note on majorization and range inclusion of adjointable operators on Hilbert \(C^\ast\)-modules ⋮ Douglas factorization theorem revisited ⋮ Solutions to some systems of adjointable operator equations over Hilbert \(C^\ast\)-modules ⋮ Factorization and range inclusion of adjointable operators on the weighted Hilbert C^∗-modules ⋮ On \(K\)-frame generators for unitary systems in Hilbert \(C^\ast\)-modules ⋮ Positivity of $2\times2$ block matrices of operators ⋮ Solutions to the system of operator equations \(A_1 X = C_1\), \(X B_2 = C_2\), and \(A_3 X B_3 = C_3\) on Hilbert \(C^*\)-modules ⋮ Sum of K-frames in Hilbert C*-modules

Cites Work

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• Common Hermitian and positive solutions to the adjointable operator equations \(AX = C\), \(XB = D\)
• The realization of multiplier Hilbert bimodule on bidual space and Tietze extension theorem
• The induced representation of \(C^*\)-groupoid dynamic systems
• Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
• Positive semi-definite matrices of adjointable operators on Hilbert \(C^{*}\)-modules
• Positive and real-positive solutions to the equationaxa*=cinC*-algebras
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space

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