# On linear continuous operators between distinguished spaces $$C_p(X)$$

@article{Kakol2021OnLC,
title={On linear continuous operators between distinguished spaces \$\$C\_p(X)\$\$},
author={Jerzy Kakol and Arkady Leiderman},
journal={Revista de la Real Academia de Ciencias Exactas, F{\'i}sicas y Naturales. Serie A. Matem{\'a}ticas},
year={2021}
}
• Published 9 July 2021
• Mathematics
• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
As proved in [16], for a Tychonoff space X , a locally convex space Cp(X) is distinguished if and only if X is a ∆-space. If there exists a linear continuous surjective mapping T : Cp(X) → Cp(Y ) and Cp(X) is distinguished, then Cp(Y ) also is distinguished [17]. Firstly, in this paper we explore the following question: Under which conditions the operator T : Cp(X) → Cp(Y ) above is open? Secondly, we devote a special attention to concrete distinguished spaces Cp([1, α]), where α is a countable…
1 Citations
A note on Banach spaces $E$ admitting a continuous map from $C_p(X)$ onto $E_{w}$
• Mathematics
• 2021
Cp(X) denotes the space of continuous real-valued functions on a Tychonoff space X endowed with the topology of pointwise convergence. A Banach space E equipped with the weak topology is denoted by

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