We explore a condition under which the ideal of polynomials generated by an ideal of multilinear mappings between Banach spaces is a global holomorphy type. After some examples and applications, this condition is studied in its own right. A final section provides applications to the ideals formed by multilinear mappings and polynomials which are absolutely (p;q)-summing at every point.
In this paper spaces of entire functions of -holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we “construct an algorithm” to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions. Annales...
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables