Vector-Valued Integration in -Spaces

  • A. Pechtl

    Universität Stuttgart, Germany


Questions of convergence in K-spaces, i.e. Banach spaces of complex-valued sequences with continuity of all functionals will be studied by methods of Fourier analysis. An elegant treatment is possible if the Cesàro sections of a -space element 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 -spaces which are generated by a given -space.

Cite this article

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

DOI 10.4171/ZAA/684