Operator equations \(AX+YB=C\) and \(AXA^\ast + BYB^\ast =C\) in Hilbert \(C^\ast\)-modules

DOI10.1016/j.laa.2016.12.001zbMath1355.15013OpenAlexW2560569885MaRDI QIDQ503417

Yong-Cai Geng, Sumit K. Garg

Publication date: 12 January 2017

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.12.001

zbMATH Keywords

solutionmatrix equationoperator equationHilbert \(C^\ast\)-moduleorthogonally complemented

Mathematics Subject Classification ID

Matrix equations and identities (15A24) (C^*)-modules (46L08) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Equations involving linear operators, with operator unknowns (47A62) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (8)

Unnamed Item ⋮ 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 ⋮ Pedersen-Takesaki operator equation and operator equation \(AX = B\) in Hilbert \(C^*\)-modules ⋮ On majorization and range inclusion of operators on Hilbert C*-modules ⋮ Douglas factorization theorem revisited ⋮ Vector-valued reproducing kernel Hilbert \(C^*\)-modules ⋮ Solutions of the Sylvester equation in \(C^*\)-modular operators

Cites Work

• On the Hermitian solutions to a system of adjointable operator equations
• Solutions to operator equations on Hilbert \(C^*\)-modules. II
• Solutions to operator equations on Hilbert \(C^*\)-modules
• The matrix equation AXB+CYD=E
• The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\)
• The matrix equation \(AX-YB=C\)
• On solutions of matrix equation \(AXB+CYD=F\)
• Positive semi-definite matrices of adjointable operators on Hilbert \(C^{*}\)-modules
• On operator ranges
• Positive definite solutions of certain nonlinear matrix equations
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
• Unnamed Item
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