Operators on the stopping time space

Dimitris Apatsidis

Studia Mathematica, Tome 231 (2015), p. 235-258 / Harvested from The Polish Digital Mathematics Library

Résumé

Let S¹ be the stopping time space and ℬ₁(S¹) be the Baire-1 elements of the second dual of S¹. To each element x** in ℬ₁(S¹) we associate a positive Borel measure $μ_{x * *}$ on the Cantor set. We use the measures $μ_{x * *} : x * * \in ℬ ₁ (S ¹)$ to characterize the operators T: X → S¹, defined on a space X with an unconditional basis, which preserve a copy of S¹. In particular, if X = S¹, we show that T preserves a copy of S¹ if and only if $μ_{T * * (x * *)} : x * * \in ℬ ₁ (S ¹)$ is non-separable as a subset of $ℳ (2^{ℕ})$ .

Publié le : 2015-01-01

Zbl 06526957

EUDML-ID : urn:eudml:doc:285424

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     author = {Dimitris Apatsidis},
     title = {Operators on the stopping time space},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {235-258},
     zbl = {06526957},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-3-3}
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Dimitris Apatsidis. Operators on the stopping time space. Studia Mathematica, Tome 231 (2015) pp. 235-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-3-3/