Positive solutions to operator equations \(AXB=C\)

DOI10.1016/j.laa.2010.05.001zbMath1200.47023OpenAlexW2021752762MaRDI QIDQ989060

M. Laura Arias, María Celeste Gonzalez

Publication date: 27 August 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.2010.05.001

zbMATH Keywords

positive solutionsgeneralized inversesoperator equation

Mathematics Subject Classification ID

Equations involving linear operators, with operator unknowns (47A62) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (17)

Hermitian solutions to the system of operator equations T_iX=U_i. ⋮ Note on the assumptions in working with generalized inverses ⋮ On the solutions of the operator equation XAX  =  BX ⋮ Solvability of \(A_iXB_i=C_i\), \(i=\overline{1,2}\), with applications to inequality \(C{\mathop{\leq}\limits^\ast}AXB\) ⋮ Computing elements of certain form in ideals to prove properties of operators ⋮ Weighted least squares solutions of the equation \(AXB-C=0\) ⋮ Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law ⋮ Algorithm for inequality-constrained least squares problems ⋮ Douglas' + Sebestyén's lemmas = a tool for solving an operator equation problem ⋮ Toward solution of matrix equation \(X=Af(X)B+C\) ⋮ Unnamed Item ⋮ A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications ⋮ Operator algebra generated by an element from the module \(\mathcal {B}(V_1,V_2)\) ⋮ Solutions to the system of operator equations \(A X B = C = B X A\) ⋮ Positivity of $2\times2$ block matrices of operators ⋮ Shorted operators and minus order ⋮ Solvability and different solutions of the operator equation \(XAX=BX\)

Cites Work

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• Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C
• Generalized inverses and Douglas equations
• Inner, outer, and generalized inverses in banach and hilbert spaces
• Shorted Operators. II
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• 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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