The Blum-Hanson Property

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2019-01-01 DOI:10.1515/conop-2019-0009
S. Grivaux
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Abstract

Abstract Given a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, y ∈ X are such that Tnx tends weakly to y in X as n tends to infinity, the means 1N∑k=1NTnkx {1 \over N}\sum\limits_{k = 1}^N {{T^{{n_k}}}x} tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lefèvre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lefèvre-Matheron, we characterize the compact metric spaces K such that the space C(K) has the Blum-Hanson property.
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Blum-Hanson物业
摘要给定一个(实的或复的,可分离的)Banach空间和X上的收缩T,我们说T具有Blum-Hanson性质,如果当X,y∈X使得Tnx在X中弱趋向于y,因为n趋向于无穷大,则对于每个严格递增的整数序列(nk)k≥1,均值1N∑k=1NTnkx{1\overN}\sum\limits_{k=1}^n{{T^{n_k}}X}趋向于y。空间X本身具有Blum-Hanson性质,如果X上的每个收缩都具有Blum-汉森性质。我们解释了Blum-Hanson性质的遍历理论动机,证明了Hilbert空间具有Blum-Hansson性质,然后由于Lefèvre Matheron Primot,提出了一个最近的几何风格标准,它允许检索基本上所有已知的具有Blum-汉森性质的空间的例子。最后,继Lefèvre Matheron之后,我们刻画了紧致度量空间K,使得空间C(K)具有Blum-Hanson性质。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
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