An extension result for (LB)-spaces and the surjectivity of tensorized mappings

Andreas Debrouwere, Lenny Neyt

Onderzoeksoutput: Articlepeer review

Samenvatting

We study an extension problem for continuous linear maps in the setting of (LB)-spaces. More precisely, we characterize the pairs (E, Z), where E is a locally complete space with a fundamental sequence of bounded sets and Z is an (LB)-space, such that for every exact sequence of (LB)-spaces [Equation not available: see fulltext.]the map L(Y,E)→L(X,E),T↦T∘ι is surjective, meaning that each continuous linear map X→ E can be extended to a continuous linear map Y→ E via ι , under some mild conditions on E or Z (e.g. one of them is nuclear). We use our extension result to obtain sufficient conditions for the surjectivity of tensorized maps between Fréchet-Schwartz spaces. As an application of the latter, we study vector-valued Eidelheit type problems. Our work is inspired by and extends results of Vogt [24].

Originele taal-2English
TijdschriftAnnali di Matematica Pura ed Applicata
DOI's
StatusPublished - 2024

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Publisher Copyright:
© 2024, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

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