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PROOF MINING IN Lp SPACES

Published online by Cambridge University Press:  29 August 2019

ANDREI SIPOŞ
Affiliation:
DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRASSE 7, 64289 DARMSTADT, GERMANY and SIMION STOILOW INSTITUTE OF MATHEMATICS OF THE ROMANIAN ACADEMY CALEA GRIVIŢEI 21, 010702BUCHAREST, ROMANIA E-mail: sipos@mathematik.tu-darmstadt.de Current address: DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRASSE 7, 64289DARMSTADT, GERMANY
Corresponding

Abstract

We obtain an equivalent implicit characterization of Lp Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for such spaces into a higher order logical system, the kind of which is used in proof mining, a research program that aims to obtain the hidden computational content of mathematical proofs using tools from mathematical logic. As an aside, we obtain a concrete way of formalizing Lp spaces in positive-bounded logic. The axiomatization is followed by a corresponding metatheorem in the style of proof mining. We illustrate its use with the derivation for this class of spaces of the standard modulus of uniform convexity.

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Copyright
Copyright © The Association for Symbolic Logic 2019 

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