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• # Artykuł - szczegóły

## Studia Mathematica

2016 | 232 | 3 | 243-266

## Tameness in Fréchet spaces of analytic functions

EN

### Abstrakty

EN
A Fréchet space 𝓧 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 𝓧 into itself, there exist N₀ and C > 0 such that
$||T(x)||ₙ ≤ C||x||_{σ(n)}$ ∀x ∈ 𝓧, n ≥ N₀.
This property does not depend upon the choice of the fundamental system of seminorms for 𝓧 and is a property of the Fréchet space 𝓧. In this paper we investigate tameness in the Fréchet spaces 𝓞(M) of analytic functions on Stein manifolds M equipped with the compact-open topology. Actually we will look into tameness in the more general class of nuclear Fréchet spaces with properties $\underline{DN}$ and Ω of Vogt and then specialize to analytic function spaces. We show that for a Stein manifold M, tameness of 𝓞(M) is equivalent to hyperconvexity of M.

243-266

wydano
2016

### Twórcy

autor
• Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bulvarı, 06800, Çankaya, Ankara, Turkey