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Zeitschrift für Analysis und ihre Anwendungen

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Volume 15, Issue 1, 1996, pp. 7–18
DOI: 10.4171/ZAA/684

Published online: 1996-03-31

Vector-Valued Integration in $BK$-Spaces

A. Pechtl[1]

(1) Universität Stuttgart, Germany

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.

Keywords: $BK$-spaces, Riemann integration, Cesàro-sectional (weak) convergence and boundedness

Pechtl A.: Vector-Valued Integration in $BK$-Spaces. Z. Anal. Anwend. 15 (1996), 7-18. doi: 10.4171/ZAA/684