Uniform Versions of Infinitary Properties in Banach Spaces

Details Uniform Versions of Infinitary Properties in Banach Spaces Uniform Versions of Infinitary Properties in Banach Spaces

1999-05-11

arxiv.org/abs/math/9905061v1

Mathematics

Logic

Latex2e, 27 pages

Scientific paper

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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