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On complemented copies of the space c0 in spaces Cp(X,E)C_p(X,E)
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SYSNO ASEP 0582703 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On complemented copies of the space c0 in spaces Cp(X,E)C_p(X,E) Author(s) Bargetz, Ch. (IL)
Kąkol, Jerzy (MU-W) SAI, RID, ORCID
Sobota, D. (AT)Source Title Mathematische Nachrichten - ISSN 0025-584X
Roč. 297, č. 2 (2024), s. 644-656Number of pages 13 s. Publication form Print - P Language eng - English Country DE - Germany Keywords Josefson-Nissenzweig Theorem ; locally convex spaces ; separately continuous functions Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GF20-22230L GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support MU-W - RVO:67985840 UT WOS 001067375000001 EID SCOPUS 85170672560 DOI https://doi.org/10.1002/mana.202300026 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2025 Electronic address https://doi.org/10.1002/mana.202300026
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