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
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.
he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.
The relationships between the JB*-triple structure of a complex spin factor S and the structure of the Hilbert space H associated to S are discussed. Every surjective linear isometry L of S can be uniquely represented in the form L(x) = mu.U(x) for some conjugation commuting unitary operator U on H and some mu belonging to C, |mu|=1. Automorphisms of S are characterized as those linear maps (continuity not assumed) that preserve minimal tripotents in S and the orthogonality relations among them.
Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory...
We study the Kergin operator on the space of nuclearly entire functions of bounded type on a Banach space E. We show that the Kergin operator is a projector with interpolating properties and that it preserves homogeneous solutions to homogeneous differential operators. Further, we show that the Kergin operator is uniquely determined by these properties. We give error estimates for approximating a function by its Kergin polynomial and show in this way that for any given bounded sequence of interpolation...
Starting from Lagrange interpolation of the exponential function in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space . Given such a representable entire funtion , in order to study the approximation problem and the uniform convergence of these polynomials to on bounded sets of , we present a sufficient growth condition on the interpolating...