On complemented copies of the space c0 in spaces Cp(X,E)C_p(X,E)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00582703" target="_blank" >RIV/67985840:_____/24:00582703 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mana.202300026" target="_blank" >https://doi.org/10.1002/mana.202300026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.202300026" target="_blank" >10.1002/mana.202300026</a>

Result language
angličtina
Original language name
On complemented copies of the space c0 in spaces Cp(X,E)C_p(X,E)
Original language description
We study the question for which Tychonoff spaces X and locally convex spaces E the space (Formula presented.) of continuous E-valued functions on X contains a complemented copy of the space (Formula presented.), both endowed with the pointwise topology. We provide a positive answer for a vast class of spaces, extending classical theorems of Cembranos, Freniche, and Domański and Drewnowski, proved for the case of Banach and Fréchet spaces (Formula presented.). Also, for given infinite Tychonoff spaces X and Y, we show that (Formula presented.) contains a complemented copy of (Formula presented.) if and only if any of the spaces (Formula presented.) and (Formula presented.) contains such a subspace.
Czech name
—
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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