巴拿赫空间中无穷性质的统一形式
Uniform Versions of Infinitary Properties in Banach Spaces
摘要：
在泛函分析中，它是感兴趣的研究以下一般性问题：是统一版本的财产，在所有巴拿赫空间也有效的所有巴拿赫空间？上述问题的肯定答案的例子是著名的等距定理的几乎等距版本的证明主机。另一个例子是罗森塔尔的克里文定理的统一版本。使用扩展版本的Henson的紧性结果的正有界公式在赋范结构，我们表明，上述问题的答案实际上是肯定的每一个属性，可以表示在一个特定的无穷语言。
英文摘要：
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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