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Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E 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

Seppo Hiltunen (1999)

Studia Mathematica

We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller C Π k -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.

Infinite dimensional Gegenbauer functionals

Abdessatar Barhoumi, Habib Ouerdiane, Anis Riahi (2007)

Banach Center Publications

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 β , 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 β by using the so-called β-type Wick product.

Infinitely divisible cylindrical measures on Banach spaces

Markus Riedle (2011)

Studia Mathematica

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on...

Integral holomorphic functions

Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)

Studia Mathematica

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.

Integral polynomials on Banach spaces not containing ℓ 1

Raffaella Cilia, Joaquín M. Gutiérrez (2010)

Czechoslovak Mathematical Journal

We give new characterizations of Banach spaces not containing ℓ 1 in terms of integral and p -dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.

Integrals and Banach spaces for finite order distributions

Erik Talvila (2012)

Czechoslovak Mathematical Journal

Let ℬ c denote the real-valued functions continuous on the extended real line and vanishing at - ∞ . Let ℬ r denote the functions that are left continuous, have a right limit at each point and vanish at - ∞ . Define 𝒜 c n to be the space of tempered distributions that are the n th distributional derivative of a unique function in ℬ c . Similarly with 𝒜 r n from ℬ r . A type of integral is defined on distributions in 𝒜 c n and 𝒜 r n . The multipliers are iterated integrals of functions of bounded variation. For each n ∈ ℕ , the spaces...

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