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An application of Kadets renorming theorem to vector-valued Riemann integrability

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We use Kadets renorming theorem in separable Banach spaces to characterize Darboux integrable vector valued functions in terms of Riemann integrable functions.

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Acknowledgments

We thank professors V. Zizler and V. Montesinos for their suggestions in writing this note. We thank, too, a referee who helped to improve the manuscript. In particular, he/she suggested the two questions appearing (in bold) in the text. The solution to one of them appears above (Proposition 5). We thank R. J. Smith (he provided an example of an equivalent norm on \(\ell _1\) failing property (P)) and P. Hájek for fruitful discussions on this particular subject.

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  1. Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 , Valencia, Spain

    Rosario Ruiz de Cenzano

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  1. Rosario Ruiz de Cenzano
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Correspondence to Rosario Ruiz de Cenzano.

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Ruiz de Cenzano, R. An application of Kadets renorming theorem to vector-valued Riemann integrability. RACSAM 108, 861–865 (2014). https://doi.org/10.1007/s13398-013-0147-1

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  • DOI: https://doi.org/10.1007/s13398-013-0147-1

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