Holomorphic automorphisms of the unit ball of a direct sum
We endow the direct sum of two complex Banach spaces with a suitable norm, and we investigate the orbit of the origin for the group of holomorphic automorphisms of the outcoming unit ball.
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...
Holomorphic Functions and the (BB)-Property.
Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Holomorphic functions on Fréchet spaces with Schauder basis.
Holomorphic functions on fully nuclear spaces
Holomorphic functions on strict inductive limits of Banach spaces.
In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Holomorphic isometries of Cartan domains of type four
The holomorphic isometries for the Kobayashi metric of Cartan domains of type four are characterized.
Holomorphic mappings of uniformly bounded type and the linear topological invariants , and .
Holomorphic semigroups of holomorphic isometries
A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.
Holomorphically Dependent Generalised Inverses.
Holomorphy types and ideals of multilinear mappings
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.
Holomorphy types and spaces of entire functions of bounded type on Banach spaces
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...
Homeomorphic measures on products of intervals.
Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
How to define "convex functions" on differentiable manifolds
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.
Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type
Hypercyclicity of convolution operators on spaces of entire functions
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
Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces
We show that a Banach space has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.
Implicit functions from locally convex spaces to Banach spaces
We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.