The Relationship between Two Involutive Semigroups S and ST Is Defined by a Left Multiplier T. (14th August 2014) - Mohammadi, S. M.; Laali, J.
Abstract : LetS be a semigroup with a left multiplier T onS . There exists a new semigroupS T, which depends onS and T, which has the same underlying space asS . We study the question of involutions onS T and a Banach algebraA T . We find a condition of T under whichS T and the second dualA T * * * * admit an involution. We will show thatA T isC * -algebra if and only ifT : A T → A is an isometry, under mild conditions. Also, A isC * -algebra if and only if so isA T, under other minor conditions.