Disjoint strict singularity of inclusions between rearrangement invariant spaces
| dc.contributor.author | Hernández, Francisco L. | |
| dc.contributor.author | Sánchez de los Reyes, Víctor Manuel | |
| dc.contributor.author | Semenov, Evgeny M. | |
| dc.date.accessioned | 2023-06-20T17:10:56Z | |
| dc.date.available | 2023-06-20T17:10:56Z | |
| dc.date.issued | 2001 | |
| dc.description | The authors wish to thank the referee for his suggestions and detailed remarks. | |
| dc.description.abstract | It is studied when inclusions between rearrangement invariant function spaces on the interval [0, infinity) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions L 1 ∩L ∞ ↪E and E↪L 1 +L ∞ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES | |
| dc.description.sponsorship | RFFI | |
| dc.description.sponsorship | Universities of Russia | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19909 | |
| dc.identifier.doi | 10.4064/sm144-3-2 | |
| dc.identifier.issn | 0039-3223 | |
| dc.identifier.officialurl | https://bit.ly/2N3hVnm | |
| dc.identifier.relatedurl | http://journals.impan.gov.pl/sm/index.html | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57903 | |
| dc.issue.number | 3 | |
| dc.journal.title | Studia Mathematica | |
| dc.language.iso | eng | |
| dc.page.final | 226 | |
| dc.page.initial | 209 | |
| dc.publisher | Polish Acad Sciencies Inst Mathematics | |
| dc.relation.projectID | PB97-0240 | |
| dc.relation.projectID | 98-01-00044 | |
| dc.relation.projectID | 3667 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Rearrangement invariant function spaces | |
| dc.subject.keyword | Inclusion operator | |
| dc.subject.keyword | Strictly singular | |
| dc.subject.keyword | Weakly compact | |
| dc.subject.keyword | Lorentz and Marcinkiewicz spaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Disjoint strict singularity of inclusions between rearrangement invariant spaces | |
| dc.type | journal article | |
| dc.volume.number | 144 | |
| dcterms.references | S. V. Astashkin, Disjoint strict singularity of embeddings of symmetric spaces, Mat. Zametki 65 (1999), 3–14 (in Russian); English transl.: Math. Notes 65 (1999), 3–12. B. Beauzamy, Espaces d'Interpolation Réels: Topologie et Géométrie, Lecture Notes on Math. 666, Springer, 1978. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, 1976. N. L. Carothers and S. J. Dilworth, Geometry of Lorentz spaces via interpolation, in: Longhorn Notes, The University of Texas at Austin, Functional Analysis Seminar (1985-6), 107–133. N. L. Carothers, S. J. Dilworth, Subspaces of L p,q , Proc. Amer. Math. Soc. 104 (1988), 537–545. F. Cobos, A. Manzano, A. Martínez and P. Matos, On interpolation of strictly singular operators, strictly cosingular operators and related operator ideals, Proc. Roy. Soc. Edinburgh, to appear. cf. A. García del Amo, F. L. Hernández and C. Ruiz, Disjointly strictly singular operators and interpolation, ibid. 126 (1996), 1011–1026. A. García del Amo, F. L. Hernández, V. M. Sánchez and E. M. Semenov, Disjointly strictly-singular inclusions between rearrangement invariant spaces, J. London Math. Soc. 62 (2000), 239–252. F. L. Hernández and B. Rodríguez-Salinas, On ℓ p -complemented copies in Orlicz spaces II, Israel J. Math. 68 (1989), 27–55. N. J. Kalton, Orlicz sequence spaces without local convexity, Math. Proc. Cambridge Philos. Soc. 81 (1977), 253–277. N. J. Kalton, personal communication, 1996. A. Kamińska and M. Mastyło, The Dunford-Pettis property for symmetric spaces, Canad. J. Math. 52 (2000), 789–803. S. G. Kreĭn, Ju. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Amer. Math. Soc., Providence, 1982. S. A. Kuzin-Aleksinskiĭ, Weakly compact embeddings of symmetric spaces, Siberian Math. J. 28 (1987), 111–113. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Sequence Spaces, Springer, 1977. J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Function Spaces, Springer, 1979. S. Ya. Novikov, Boundary spaces for inclusion map between rearrangement invariant spaces, Collect. Math. 44 (1993), 211–215. S. Ya. Novikov, The differences of inclusion map operators between rearrangement invariant spaces on finite and σ -finite measure spaces, ibid. 48 (1997), 725–732. E. I. Pustylnik, Some structural properties of the totality of intermediate spaces of a Banach couple, in: Theory of Operators in Function Spaces, Voronezh Gos. Univ., 1983, 80–89 (in Russian). D. Przeworska-Rolewicz and S. Rolewicz, Equations in Linear Spaces, Polish Sci. Publ., Warszawa, 1968. J. Y. T. Woo, On modular sequence spaces, Studia Math. 48 (1973), 271–289. | |
| dspace.entity.type | Publication |
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