Continuous linear images of spaces Cp(X) with the weak topology

0558105 - MÚ 2023 RIV ES eng J - Journal Article
Kąkol, Jerzy - Leiderman, A. G.
Continuous linear images of spaces Cp(X) with the weak topology.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 116, č. 3 (2022), č. článku 129. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Cp(X) space * continuous linear map * metrizable locally convex space * weak topology
OECD category: Pure mathematics
Impact factor: 2.9, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s13398-022-01250-4

Cp(X) denotes the space of continuous real-valued functions on a Tychonoff space X with the topology of pointwise convergence. A locally convex space (lcs) E with the weak topology is denoted by Ew. First, we show that there is no a sequentially continuous linear surjection T: Cp(X) → Ew, if E is a lcs with a fundamental sequence of bounded sets. Second, we prove that if there exists a sequentially continuous linear map from Cp(X) onto Ew for some infinite-dimensional metrizable lcs E, then the completion of E is isomorphic to the countable power of the real line Rω. Illustrating examples are provided.
Permanent Link: http://hdl.handle.net/11104/0331902