On complementability of c α in spaces C(K x L )

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00588552" target="_blank" >RIV/67985840:_____/24:00588552 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/16262" target="_blank" >https://doi.org/10.1090/proc/16262</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16262" target="_blank" >10.1090/proc/16262</a>

Result language
angličtina
Original language name
On complementability of c α in spaces C(K x L )
Original language description
Using elementary probabilistic methods, in particular a variant of theWeak Law of Large Numbers related to the Bernoulli distribution, we prove that for every infinite compact spaces K and L the product K × L admits a sequence (μn : n ∈ N) of normalized signed measures with finite supports which converges to 0 with respect to the weak*topology of the dual Banach space C(K × L)*. Our approach is completely constructive-the measures μn are defined by an explicit simple formula. We also show that this result generalizes the classical theorem of Cembranos [Proc. Amer. Math. Soc. 91 (1984), pp. 556-558] and Freniche [Math. Ann. 267 (1984), pp. 479-486] which states that for every infinite compact spaces K and L the Banach space C(K × L) contains a complemented copy of the space c0.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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