first hachschild cohomology group of triangular banach algebras on induced semigroup algebras

Let s be a discrete semigroup with a left multiplier operator ton s. a new product on s dened by t related to s and t creates a newinduced semigroup st . suppose that t is bijective andt1 =[.1(s) .1(s).1(s)]and t2 =[.1(st ) .1(st ).1(st )]:in this paper, we show that the rst cohomology groups h1(t1; t 1 ) andh1(t2; t 2 ) are equal. therefore t1 is weakly amenable if and only if t2 isweakly amenable.