A Fréchet space with a sequence 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 ∀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 topology. Actually we will look into tameness in the more general class of nuclear Fréchet spaces with properties and Ω of Vogt and then specialize to analytic function spaces. We show that for a Stein manifold M, tameness of (M) is equivalent to hyperconvexity of M.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8423-3-2016,
author = {Ayd\i n Aytuna},
title = {Tameness in Fr\'echet spaces of analytic functions},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {243-266},
zbl = {06586862},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8423-3-2016}
}
Aydın Aytuna. Tameness in Fréchet spaces of analytic functions. Studia Mathematica, Tome 233 (2016) pp. 243-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8423-3-2016/