JournalszaaVol. 15, No. 1pp. 7–18

Vector-Valued Integration in BKBK-Spaces

  • A. Pechtl

    Universität Stuttgart, Germany
Vector-Valued Integration in $BK$-Spaces cover
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Abstract

Questions of convergence in BBK-spaces, i.e. Banach spaces of complex-valued sequences x=(xk)kZx = (x_k)_{k \in \mathbb Z} with continuity of all functionals xxk((kZ)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 BKBK-space element xx 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 BKBK-spaces which are generated by a given BKBK-space.

Cite this article

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

DOI 10.4171/ZAA/684