Tameness in Fréchet spaces of analytic functions

Aydın Aytuna. "Tameness in Fréchet spaces of analytic functions." Studia Mathematica 232.3 (2016): 243-266. <http://eudml.org/doc/286684>.

@article{AydınAytuna2016,
abstract = {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 $||T(x)||ₙ ≤ C||x||_\{σ(n)\}$ ∀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 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 (M) is equivalent to hyperconvexity of M.},
author = {Aydın Aytuna},
journal = {Studia Mathematica},
keywords = {tameness of Fréchet spaces; analytic function spaces; linear topological invariants},
language = {eng},
number = {3},
pages = {243-266},
title = {Tameness in Fréchet spaces of analytic functions},
url = {http://eudml.org/doc/286684},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Aydın Aytuna
TI - Tameness in Fréchet spaces of analytic functions
JO - Studia Mathematica
PY - 2016
VL - 232
IS - 3
SP - 243
EP - 266
AB - 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 $||T(x)||ₙ ≤ C||x||_{σ(n)}$ ∀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 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 (M) is equivalent to hyperconvexity of M.
LA - eng
KW - tameness of Fréchet spaces; analytic function spaces; linear topological invariants
UR - http://eudml.org/doc/286684
ER -