Multipliers on Fréchet algebra

This paper is devoted to establish some fundamentally important results on a commutative semi simple Fréchet algebra. It has been shown that a multiplier on a semi simple Fréchet algebra is a product of an idempotent and an invertible multiplier. It has also been shown that a multiplier on a commutative semi simple Fréchet algebra which is also a Fredholm operator is a product of an idempotent and an invertible element of a continuous linear self mapping of commutative semi simple Fréchet algebra. Finally have shown that for a multiplier T on a commutative semi simple Fréchet algebra A, T2(A) is closed iff T(A) + Ker (T) is closed, T(A) + Ker(T) is closed iff A=T(A)+Ker(T)and T is a product of an idempotent and an invertible multiplier iff = T(A)+Ker(T).