关于第一贝叶尔函数的某些类别

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-09-16 DOI:10.1007/s10474-024-01464-5

J. Mirmina, D. Puglisi

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引用次数: 0

摘要

我们研究了可分离巴纳赫空间 \(X\) 对偶球上的第一贝雷函数，这些函数是 \(X\) 序列的点极限，其闭展不包含 \(\ell_1\) 的任何副本（或具有可分离对偶）。我们提出了一个 \(C(K)\) 空间的例子，在这个空间中，并非所有这样的第一拜尔函数都表现出这种行为。作为应用，我们从描述集合论的角度研究了具有这种特性的可分离巴拿赫空间族的定量版本。

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On certain classes of first Baire functionals

We investigate first Baire functionals on the dual ball of a separable Banach space \(X\) which are pointwise limit of a sequence of \(X\) whose closed span does not contain any copy of \(\ell_1\) (or has separable dual). We propose an example of a \(C(K)\) space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.