R. Muhammad, A. (2012). On the Solvability of the Operator Equation ATT*BC. Alustath, 15(2), 156-160.
Amina R. Muhammad. "On the Solvability of the Operator Equation ATT*BC". Alustath, 15, 2, 2012, 156-160.
R. Muhammad, A. (2012). 'On the Solvability of the Operator Equation ATT*BC', Alustath, 15(2), pp. 156-160.
R. Muhammad, A. On the Solvability of the Operator Equation ATT*BC. Alustath, 2012; 15(2): 156-160.

On the Solvability of the Operator Equation ATT*BC

Journal of Al-Nahrain University - Science
Article 1, Volume 15, Issue 2, June 2012, Pages 156-160
Author
Amina R. Muhammad
Abstract
In this paper we study the solvability of the operator equation
AT+T*B=C
for linear bounded operators on Hilbert space, where T is the unknown operator.
First we show this equation may not have a solution in B(H), and then we show that this equation have a simple solution in case A,B are Hermitian or Skew-Hermitian operators. Finaly we study the solvability of the operator equation AT+T*B=f(A) in case A and B are normal operators.
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