2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68272We establish lower bounds for norms and CB-norms of elementary operators on B(H). Our main result concerns the operator Tx = axb + bxa and we show its norm is at least the product of the norms of a and b, proving a conjecture of M. Mathieu. We also establish some other results and formulae for the CB norm and norm of such T for special cases.To appear in Bull Sci MathOperator Algebras47B47, 46L07, 47L25text