Solvability of \(AXB - CXD = E\) in the operators algebra \(B(H)\)

DOI10.1134/S1995080210030091zbMath1300.47023OpenAlexW2470020535MaRDI QIDQ694356

M. C. Fu

Publication date: 12 December 2012

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080210030091

zbMATH Keywords

generalised derivationmatrix and operator equationsPutnam-Fuglede's property

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Commutators, derivations, elementary operators, etc. (47B47) Equations involving linear operators, with operator unknowns (47A62)

Related Items (6)

Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm

Cites Work

• Unnamed Item
• On the operator equation \(AXB - XD = E\)
• On the operator equation \(BX - XA = Q\)
• Properties which normal operators share with normal derivations and related operators
• Another version of Maher's inequality
• Über die Unbeschränktheit der Operatoren der Quantenmechanik
• Commutator Approximants
• On the matrix equations $AX - XB = C$ and $AX - YB = C$
• Putnam-Fuglede theorem and the range-kernel orthogonality of derivations

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