Far Eastern Mathematical Journal

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On linear continuous operators on $C_p$-spaces

Devyatkov A.P., Shalaginov S.D.

2021, issue 1, P. 45-50 DOI: https://doi.org/10.47910/FEMJ202104

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.

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

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References

[1] V. Tkachuk, A Cp-theory problem book. V. I-IV, Problem Books in Mathematics, Springer, 2011–2015. [2] A. V. Arkhangel'skii, Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989. [3] Kh. Shefer, Topologicheskie vektornye prostranstva, Mir, M., 1971. [4] C. C. Kutateladze, Osnovy funktsional'nogo analiza, Izdatel'stvo Instituta matematiki, Novosibirsk, 2000.

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