Operator Solutions of the Multi–valued Operator Equation $$A = BXC$$
Adrian Sandovici · Bulletin of the Malaysian Mathematical Sciences Society · 2025
Abstract Assume that A, B and C are three linear relations on certain linear spaces. The main objective of this note is to present some necessary and sufficient conditions for the existence of the solutions X of the operator equation $$A = BXC$$ A = B X C . The obtained characterizations extend and complete some known operator factorization results due to R.G. Douglas, Z. Sebestyén and D. Popovici.