PROOF MINING IN Lp SPACES
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AbstractWe 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.
2014 ◽
Vol 66
(2)
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pp. 373-386
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2001 ◽
Vol 256
(1)
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pp. 39-44
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1963 ◽
Vol 13
(2)
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pp. 365-373
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Keyword(s):