Feral dual spaces and (strongly) distinguished spaces C(X)

0571369 - MÚ 2024 RIV DE eng J - Journal Article
Kąkol, Jerzy - Śliwa, W.
Feral dual spaces and (strongly) distinguished spaces C(X).
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 117, č. 3 (2023), č. článku 94. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : bidual space * distinguished space * fundamental family of bounded sets
OECD category: Pure mathematics
Impact factor: 2.9, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s13398-023-01417-7

Following Dieudonné and Schwartz a locally convex space is distinguished if its strong dual is barrelled. The distinguished property for spaces Cp(X) of continuous real-valued functions over a Tychonoff space X is a peculiar (although applicable) property. It is known that Cp(X) is distinguished if and only if Cp(X) is large in RX if and only if X is a Δ -space (in sense of Reed) if and only if the strong dual of Cp(X) carries the finest locally convex topology. Our main results about spaces whose strong dual has only finite-dimensional bounded sets (see Theorems 2, 7 and Proposition 4) are used to study distinguished spaces Ck(X) with the compact-open topology. We also put together several known facts (Theorem 6) about distinguished spaces Cp(X) with self-contained full proofs.
Permanent Link: https://hdl.handle.net/11104/0342606