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JOURNALS // Dal'nevostochnyi Matematicheskii Zhurnal // Archive

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.

UDC: 515.122.55+517.982.2+517.982.3

MSC: Primary 54C35; Secondary 46E10

Received: 02.03.2021

DOI: 10.47910/FEMJ202104



© Steklov Math. Inst. of RAS, 2024