Positive solutions to a system of adjointable operator equations over Hilbert \(C^*\)-modules

DOI10.1016/j.laa.2010.05.023zbMath1214.47015OpenAlexW1980763371WikidataQ112882174 ScholiaQ112882174MaRDI QIDQ5962298

Chang-Zhou Dong, Qing-Wen Wang

Publication date: 21 September 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.05.023

zbMATH Keywords

positive solutiongeneralized inverseoperator equationHilbert \(C^{*}\)-modulesystem of operator equations

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Equations involving linear operators, with operator unknowns (47A62) Positive linear operators and order-bounded operators (47B65)

Related Items (17)

Hermitian solutions to the system of operator equations T_iX=U_i. ⋮ Solving optimization problems on Hermitian matrix functions with applications ⋮ The general solutions to some systems of matrix equations ⋮ Common solutions to some operator equations over HilbertC^*–modules and applications ⋮ The \(\{P, Q, k + 1 \}\)-reflexive solution to system of matrix equations \(A X = C\), \(X B = D\) ⋮ The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations ⋮ A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations ⋮ On the Hermitian \(R\)-conjugate solution of a system of matrix equations ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ Solutions to optimization problems on ranks and inertias of a matrix function with applications ⋮ The common positive solution to adjointable operator equations with an application ⋮ A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications ⋮ Common nonnegative definite solutions of some classical matrix equations ⋮ A note on majorization and range inclusion of adjointable operators on Hilbert \(C^\ast\)-modules ⋮ Solutions to some systems of adjointable operator equations over Hilbert \(C^\ast\)-modules ⋮ 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 ⋮ The \(^*\) congruence class of the solutions to a system of matrix equations

Cites Work

• Solutions to operator equations on Hilbert \(C^*\)-modules
• Common Hermitian and positive solutions to the adjointable operator equations \(AX = C\), \(XB = D\)
• Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators
• The solutions to some operator equations
• Common Hermitian solutions to some operator equations on Hilbert \(C^{*}\)-modules
• A system of real quaternion matrix equations with applications
• Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
• The common solution to six quaternion matrix equations with applications
• The general solution to a system of real quaternion matrix equations
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Positive and real-positive solutions to the equationaxa*=cinC*-algebras
• Modules Over Operator Algebras
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