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On the Solvability of the Operator Equation ATT*BC | ||
| Journal of Al-Nahrain University - Science | ||
| Article 1, Volume 15, Issue 2, 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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