# Vector-Valued Integration in $BK$-Spaces

### A. Pechtl

Universität Stuttgart, Germany

## Abstract

Questions of convergence in $B$K-spaces, i.e. Banach spaces of complex-valued sequences $x = (x_k)_{k \in \mathbb Z}$ with continuity of all functionals $x \mapsto x_k ((k \in \mathbb Z)$ will be studied by methods of Fourier analysis. An elegant treatment is possible if the Cesàro sections of a $BK$-space element $x$ can be represented by vector-valued Riemann integrals. This was done by Goes [2] following the example of Katznelson [5: pp. 10-12). The purpose of this paper is to make precise the conditions in [2) concerning Riemann integration and to demonstrate relations between $BK$-spaces which are generated by a given $BK$-space.

## Cite this article

A. Pechtl, Vector-Valued Integration in $BK$-Spaces. Z. Anal. Anwend. 15 (1996), no. 1, pp. 7–18

DOI 10.4171/ZAA/684