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Volume 16 / Issue 18

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DOI:   10.3217/jucs-016-18-2523


A Constructive Study of Landau's Summability Theorem

Josef Berger (Ludwig-Maximilians-Universit√§t M√ľnchen, Germany)

Douglas S. Bridges (University of Canterbury, New Zealand)

Abstract: A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within Bishop-style constructive mathematics. It is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to Ishihara's principle BD-N. The paper ends with a number of results that, while not as strong as Landau's theorem, nevertheless contain positive computational information related to its conclusion.

Keywords: lp space, Landau, constructive, summability

Categories: F.4.0