On Operator Equation TA-AT*=C

Adil G. Naoum, Amina R. Al-Kabbani

Abstract


Let H  be a separable complex Hilbert space, and let B(H) be the algebra of bounded linear operators on H. Let A, B, C be elements in B(H). The equation AX-XB=C, which is called Sylvester’s equation or Rosenbium’s equation has been studied extensively by many mathematicians (see for example Bhatia and Rosenthal, 1997).

More recently, equations of the form TA-AT*=C, where T* represents the adjoint of T, began to receive more and more attention (Molnár, 1996; Molnár, 1994; Molnár, 1996; Semrl, 1994; Semrl, 1999; Semrl, 1991).

In this paper, we give necessary conditions for equation of the form TA-AT*=ƒ(A) to have a solution in case A is a normal operator.


Keywords


Normal Operator, The Equation TA-AT*=C

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