Polynomials and holomorphic functions on interpolation spaces
Preduals of spaces of vector-valued holomorphic functions
For a balanced open subset of a Fréchet space and a dual-Banach space we introduce the topology on the space of holomorphic functions from into . This topology allows us to construct a predual for which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions....
Products of holomorphically relevant spaces
Pseudodistances invariantes sur les domaines d'un espace localement convexe
Quantum Lévy-type Laplacian and associated stochastic differential equations
We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.
Quasi-completeness on the Spaces of Holomorphic Germs
Sia uno spazio riflessivo e sia un compatto di . Si dimostra che lo spazio dei germi olomorfi su , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.
Quasinormability of some spaces of holomorphic mappings.
A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.
Quasinormable spaces and the problem of topologies of Grothendieck.
Quasinormable spaces of polynomials.
Reflexivity and kernels in infinite dimensional holomorphy
Remark on analytic functions in ordered spaces
Resultados Recientes Sobre Espacios Polinomiales De Tipo Numerable.
Rigidity of holomorphic isometries
A rigidity theorem for holomorphic families of holomorphic isometries acting on Cartan domains is proved.
Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains
Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of -algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.
Rings of PDE-preserving operators on nuclearly entire functions
Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on (i.e. the continuous operators that commute with all translations) is formed by the transposes , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on is PDE-preserving for a set ℙ ⊆ Exp(F) if it...
Schauder bases and the bounded approximation property in separable Banach spaces
Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties and . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.
Schauder Type Theorems for Differentiable and Holomorphic Mappings.
Schur class operator functions and automorphisms of Hardy algebras.
Separability of analytic images of some Banach spaces
Separable quotients of Banach spaces.
In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.