Abstract
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.
Original language | English |
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Article number | 129 |
Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
Volume | 116 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jul 2022 |
Keywords
- C(X) space
- Continuous linear map
- Metrizable locally convex space
- Weak topology
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Computational Mathematics
- Applied Mathematics