Solutions to the system of operator equations \(A X B = C = B X A\)

DOI10.1016/S0252-9602(18)30804-XzbMath1438.47030WikidataQ129652745 ScholiaQ129652745MaRDI QIDQ2313131

Xiao Zhang, Guo Xing Ji

Publication date: 18 July 2019

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

solutionpositive solutionMoore-Penrose inverseoperator equationHermitian solution

Mathematics Subject Classification ID

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

Related Items (5)

Unnamed Item ⋮ Unnamed Item ⋮ Solvability of \(A_iXB_i=C_i\), \(i=\overline{1,2}\), with applications to inequality \(C{\mathop{\leq}\limits^\ast}AXB\) ⋮ Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations ⋮ The commuting inverse along an element in semigroups

Cites Work

• Unnamed Item
• The supremum of linear operators for the *-order
• On the solutions of operator equation \(CAX=C=XAC\)
• Common Hermitian and positive solutions to the adjointable operator equations \(AX = C\), \(XB = D\)
• The solutions to some operator equations
• Common Hermitian solutions to some operator equations on Hilbert \(C^{*}\)-modules
• Positive solutions to operator equations \(AXB=C\)
• On the symmetric solutions of a linear matrix equation
• Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
• Common properties of the operator products in spectral theory
• Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C
• Inner, outer, and generalized inverses in banach and hilbert spaces
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Solutions of the system of operator equations $BXA=B=AXB$ via the *-order
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space

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