Publicação
On the weak convergence of shift operators to zero on rearrangement-invariant spaces
| dc.contributor.author | Karlovych, Oleksiy | |
| dc.contributor.author | Shargorodsky, Eugene | |
| dc.contributor.institution | CMA - Centro de Matemática e Aplicações | |
| dc.contributor.institution | DM - Departamento de Matemática | |
| dc.contributor.pbl | Springer | |
| dc.date.accessioned | 2023-04-28T22:22:19Z | |
| dc.date.available | 2024-01-02T01:31:34Z | |
| dc.date.embargoedUntil | 2024-01-01 | |
| dc.date.issued | 2023-01 | |
| dc.description | Publisher Copyright: © 2022, Universidad Complutense de Madrid. | |
| dc.description.abstract | Let { hn} be a sequence in Rd tending to infinity and let {Thn} be the corresponding sequence of shift operators given by (Thnf)(x)=f(x-hn) for x∈ Rd. We prove that {Thn} converges weakly to the zero operator as n→ ∞ on a separable rearrangement-invariant Banach function space X(Rd) if and only if its fundamental function φX satisfies φX(t) / t→ 0 as t→ ∞. On the other hand, we show that {Thn} does not converge weakly to the zero operator as n→ ∞ on all Marcinkiewicz endpoint spaces Mφ(Rd) and on all non-separable Orlicz spaces LΦ(Rd). Finally, we prove that if { hn} is an arithmetic progression: hn= nh, n∈ N with an arbitrary h∈ Rd\ { 0 } , then { Tnh} does not converge weakly to the zero operator on any non-separable rearrangement-invariant Banach function space X(Rd) as n→ ∞. | en |
| dc.description.version | authorsversion | |
| dc.description.version | published | |
| dc.format.extent | 34 | |
| dc.format.extent | 398264 | |
| dc.identifier.doi | 10.1007/s13163-022-00423-4 | |
| dc.identifier.issn | 1139-1138 | |
| dc.identifier.other | PURE: 56423613 | |
| dc.identifier.other | PURE UUID: 49b5c778-cf84-4e0f-a810-a5058d847e8a | |
| dc.identifier.other | Scopus: 85126854346 | |
| dc.identifier.other | WOS: 000771853200001 | |
| dc.identifier.uri | http://hdl.handle.net/10362/152251 | |
| dc.identifier.url | https://www.scopus.com/pages/publications/85126854346 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.relation | Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT | |
| dc.subject | Fundamental function | |
| dc.subject | Limit operator | |
| dc.subject | Marcinkiewicz endpoint space | |
| dc.subject | Non-separable Orlicz space | |
| dc.subject | Rearrangement-invariant Banach function space | |
| dc.subject | Shift operator | |
| dc.subject | Weak convergence to zero | |
| dc.subject | General Mathematics | |
| dc.title | On the weak convergence of shift operators to zero on rearrangement-invariant spaces | en |
| dc.type | journal article | |
| degois.publication.firstPage | 91 | |
| degois.publication.issue | 1 | |
| degois.publication.lastPage | 124 | |
| degois.publication.title | Revista Matematica Complutense | |
| degois.publication.volume | 36 | |
| dspace.entity.type | Publication | |
| rcaap.rights | openAccess |
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