## Abstract

C_{p}(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 E_{w}. First, we show that there is no a sequentially continuous linear surjection T: C_{p}(X) → E_{w}, 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 C_{p}(X) onto E_{w} for some infinite-dimensional metrizable lcs E, then the completion of E is isomorphic to the countable power of the real line R^{ω}. 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

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