Polynomials and Multinear mappings in locally convex algebras

Abstract

We introduce the pseudo-equicontinuity of a sequence of maps in topological algebras. This notion allows us to simplify the proofs of classical results such as theorems of Turpin for power maps in commutative locally convex algebras and that of B. Mitiagin, S. Rolewics and W. Zelazko for entire functions in commutative B0-algebras. We also obtain that a commutative B0-algebra A is m-convex if a power series with an appropriate control over its coefficients operates in some open subset of A.