On the completeness of the space OC$\mathcal {O}_C$

Michael Kunzinger and Norbert Ortner

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2740-2748

Abstract: We explicitly prove the compact regularity of the LF$\mathcal {LF}$‐space of double sequences limk→(s⊗̂(ℓp)k)≅limk→(s⊗̂(c0)−k)$ {\lim _{k\rightarrow }} (s\widehat{\otimes }(\ell ^p)_{k}) \cong {\lim _{k\rightarrow }}(s\widehat{\otimes }(c_0)_{-k})$, 1≤p≤∞$1\le p\le \infty$. As a consequence, we obtain that the spaces of slowly and uniformly slowly increasing C∞$C^\infty$‐functions OM$\mathcal {O}_M$ and OC$\mathcal {O}_C$, respectively, are ultrabornological and complete. Furthermore, we prove that limk→(Ek⊗̂ιF)=(limk→Ek)⊗̂ιF$ {\lim _{k\rightarrow }}(E_k\widehat{\otimes }_\iota F) = ({\lim _{k\rightarrow }} E_k) \widehat{\otimes }_\iota F$ if the inductive limit limk→(Ek⊗̂ιF)$ {\lim _{k\rightarrow }}(E_k \widehat{\otimes }_\iota F)$ is compactly regular.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.70013

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:8:p:2740-2748

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().