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Tameness in Fréchet spaces of analytic functions

Aydın Aytuna (2016)

Studia Mathematica

A Fréchet space with a sequence | | · | | k k = 1 of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that | | T ( x ) | | C | | x | | σ ( n ) ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped with the compact-open...

The density condition in projective tensor products.

Wolf-Dieter Heinrichs (1999)

Revista Matemática Complutense

In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.

The dual of the space of holomorphic functions on locally closed convex sets.

José Bonet, Reinhold Meise, Sergej N. Melikhov (2005)

Publicacions Matemàtiques

Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.

The non-archimedian space BC(X) with the strict topology.

Nicole De Grande-De Kimpe, Samuel Navarro (1994)

Publicacions Matemàtiques

Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.

The space of real-analytic functions has no basis

Paweł Domański, Dietmar Vogt (2000)

Studia Mathematica

Let Ω be an open connected subset of d . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

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