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 Dal'nevost. Mat. Zh., 2021, Volume 21, Number 1, Pages 45–50 (Mi dvmg445)

On linear continuous operators on $C_p$-spaces

A. P. Devyatkov, S. D. Shalaginov

Tyumen State University

Abstract: The paper describes the structure of a linear continuous operator on the space of continuous functions in the topology of pointwise convergence. The corresponding theorem is a generalization of A. V. Arkhangel'skii's theorem on the general form of a continuous linear functional on such spaces.

Key words: space of continuous functions in the topology of pointwise convergence, topological vector space, locally bounded space, continuous linear operator.

DOI: https://doi.org/10.47910/FEMJ202104

Full text: PDF file (451 kB)
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UDC: 515.122.55+517.982.2+517.982.3
MSC: Primary 54C35; Secondary 46E10

Citation: A. P. Devyatkov, S. D. Shalaginov, “On linear continuous operators on $C_p$-spaces”, Dal'nevost. Mat. Zh., 21:1 (2021), 45–50

Citation in format AMSBIB
\Bibitem{DevSha21}
\by A.~P.~Devyatkov, S.~D.~Shalaginov
\paper On linear continuous operators on $C_p$-spaces
\jour Dal'nevost. Mat. Zh.
\yr 2021
\vol 21
\issue 1
\pages 45--50
\mathnet{http://mi.mathnet.ru/dvmg445}
\crossref{https://doi.org/10.47910/FEMJ202104}