R]) with the pointwise multiplication becomes a commutative Banach algebra.

The set M(A) of all multipliers of A is a unital commutative Banach algebra, called the multiplier algebra of A.

becomes a

commutative Banach algebra with the constant function 1 as the identity.

Let A be a commutative Banach algebra without order.

B]) be an abstract Segai algebra with respect to the commutative Banach algebra (A, [parallel] x [[parallel].

The converse holds, whenever A is either unital or a commutative Banach algebra.

Since SA(G) is a commutative Banach algebra, Lemma 3.

are considered in when T is a power bounded operator on a

commutative Banach algebra [?

ii) A

commutative Banach algebra is n-weakly amenable if and only if it is approximately n-weakly amenable.

A])) shows that the Gelfand transform establishes a connection between the abstract

commutative Banach algebra A and the concrete commutative [C.

Rota-Baxter operators appeared in the work of Baxter [3] on differential operators on

commutative Banach algebras, being particularly useful in relation to the Spitzer identity.

In this case every commutative Gelfand-Mazur algebra A is homomorphic/isomorphic with a subalgebra of C(homA), similarly to the case of

commutative Banach algebras.