Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order

2021/12/10 by Kruse, Karsten
#Mathematik #epsilon-product #extension #vector-valued #weak-strong principle #weight

paper · doi:10.15480/882.4017

Abstract

In this paper we study the problem of extending functions with values in a locally convex Hausdorff space E over a field K, which has weak extensions in a weighted Banach space Fν(Ω,K) of scalar-valued functions on a set Ω, to functions in a vector-valued counterpart Fν(Ω,E) of Fν(Ω,K). Our findings rely on a description of vector-valued functions as continuous linear operators and extend results of Frerick, Jordá and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.

Related

• Weighted spaces of vector-valued functions and the ε-product
• Riesz type theorem in locally convex vector spaces
• Strong vector valued integrals
• A uniformly continuous linear extension principle in topological vector spaces with an application to Lebesgue integration
• Observations on some classes of operators on C(K,X)