Tameness in Fréchet spaces of analytic functions

• Autorzy: Aydın Aytuna
• Języki publikacji: 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.

Kategorie tematyczne

• 32U15: General pluripotential theory
• 46A61: Graded Fr\'echet spaces and tame operators
• 32A70: Functional analysis techniques \SeeMainly{}
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 46A63: Topological invariants ((DN), ( Ω ), etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 3
• Strony: 243-266

Daty

wydano

2016

Twórcy

autor

Aydın Aytuna

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

Identyfikatory

DOI

10.4064/sm8423-3-2016