Uniform Versions of Infinitary Properties in Banach Spaces

1999/05/11 by Carlos Ortiz, Ortiz, Carlos · 1 citation
Mathematics · #03C65 (Primary) 46B08 #46B20 (Secondary) #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #math.FA #math.LO #msc:03C65 #msc:46B08 #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/9905061

Latex2e, 27 pages

arxiv created 1999/05/11 · openalex publication_date 1999/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In functional analysis it is of interest to study the following general question: Is the uniform version of a property that holds in all Banach spaces also valid in all Banach spaces? Examples of affirmative answers to the above question are the host of proofs of almost-isometric versions of well known isometric theorems. Another example is Rosenthal's uniform version of Krivine's Theorem. Using an extended version of Henson's Compactness result for positive bounded formulas in normed structures, we show that the answer of the above question is in fact yes for every property that can be expressed in a particular infinitary language.

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• Expressive power of infinitary [0, 1]-valued logics

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