Solvability of The Operator Equations $ AX-XB=C $ and $ AX-YB=C $

This paper provides new necessary and sufficient conditions for the solvability to the operator equations $A X - X B = C$ and $A X - Y B = C,$ where $A$ and $B$ are group invertible operators defined on an infinite dimensional Hilbert space. In addition, the general solutions to the equation $A X - Y B = C,$ are derived in terms of group inverse of $A$ and $B$ . As a consequence, new necessary and sufficient conditions for the solvability to the operator equation $A Y B - Y = C,$ are derived.

Solvability of The Operator Equations $A X - X B = C$ and $A X - Y B = C$

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Solvability of The Operator Equations $A X - X B = C$ and $A X - Y B = C$

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Solvability of The Operator Equations AX−XB=CAX−XB=C and AX−YB=CAX−YB=C

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Solvability of The Operator Equations AX−XB=CAX−XB=C and AX−YB=CAX−YB=C

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|讲解博客

|AI智能校验

Solvability of The Operator Equations $A X - X B = C$ and $A X - Y B = C$

讲解博客

AI智能校验

Solvability of The Operator Equations $A X - X B = C$ and $A X - Y B = C$

讲解博客

AI智能校验