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

0582703 - MÚ 2025 RIV DE eng J - Journal Article
Bargetz, Ch. - Kąkol, Jerzy - Sobota, D.
On complemented copies of the space c0 in spaces Cp(X,E)C_p(X,E).
Mathematische Nachrichten. Roč. 297, č. 2 (2024), s. 644-656. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Josefson-Nissenzweig Theorem * locally convex spaces * separately continuous functions
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/mana.202300026

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.
Permanent Link: https://hdl.handle.net/11104/0350787