The Relationship between Two Involutive Semigroups S and S T Is Defined by a Left Multiplier T

Abstract EN

Let S be a semigroup with a left multiplier T on S .

There exists a new semigroup S T , which depends on S and T, which has the same underlying space as S .

We study the question of involutions on S T and a Banach algebra A T .

We find a condition of T under which S T and the second dual A T * * * * admit an involution.

We will show that A T is C * -algebra if and only if T : A T → A is an isometry, under mild conditions.

Also, A is C * -algebra if and only if so is A T , under other minor conditions.