On linear continuous operators on $C_p$-spaces
Devyatkov A.P., Shalaginov S.D.
2021, issue 1, Ñ. 45-50
|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
Download the article (PDF-file)
| V. Tkachuk, A Cp-theory problem book. V. I-IV, Problem Books in Mathematics, Springer, 2011–2015.|
 A. V. Arkhangel'skii, Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989.
 Kh. Shefer, Topologicheskie vektornye prostranstva, Mir, M., 1971.
 C. C. Kutateladze, Osnovy funktsional'nogo analiza, Izdatel'stvo Instituta matematiki, Novosibirsk, 2000.