Let e a Banach algebra and suppose that and are closed two-sided ideal and closed subalgebra of , respectively. We introduce semidirect product algebra and characterize the multiplier algebra of in terms of the individual multiplier algebras of and . We then apply this result to investigate the BSE-property of these ltr" As special cases of semidirect product algebras, we study and and characterize the BSE-functions on the carrier space and , in terms of those functions on and .
