Extension of vector-valued functions and sequence space representation

Abstract

We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a space $\mathcal{F}(\Omega ,\mathbb{K})$ of scalar-valued functions on a set $\Omega$, to functions in a vector-valued counterpart $\mathcal{F}(\Omega ,E)$ of $\mathcal{F}(\Omega ,\mathbb{K})$. The results obtained base upon a representation of vector-valued functions as linear continuous operators and extend results of Bonet, Frerick, Gramsch and Jordá. In particular, we apply them to obtain a sequence space representation of $\mathcal{F}(\Omega ,E)$ from a known representation of $\mathcal{F}(\Omega ,\mathbb{K})$.

References in corpus (3)

• On natural invariant measures on generalised iterated function systems
• Weighted vector-valued functions and the $\epsilon$-product
• Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order

Cited by in corpus (2)

• On linearisation and uniqueness of preduals
• Vector-valued Fourier hyperfunctions and boundary values