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

Jerzy Ka̧kol, Arkady Leiderman

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Article number129
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Issue number3
StatePublished - 1 Jul 2022


  • C(X) space
  • Continuous linear map
  • Metrizable locally convex space
  • Weak topology

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics


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