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Some Interpolation Results that are the Exclusive Property of Compact Operators

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dc.contributor.authorCobos, Fernando
dc.contributor.authorFernández-Cabrera, Luz M.
dc.contributor.authorMartínez, Antón
dc.contributor.authorPustylnik, Evgeniy
dc.date.accessioned2023-06-20T16:50:58Z
dc.date.available2023-06-20T16:50:58Z
dc.date.issued2002
dc.description.abstractWe show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J -functionals of interpolation theory.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGES
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15147
dc.identifier.citationJ. Bergh and J. Lofstrom. Interpolation spaces. An introduction (Springer, 1976). Y. Brudnyi and N. Krugljak. Interpolation functors and interpolation spaces, vol. 1 (Amsterdam: North-Holland, 1991). F. Cobos and E. Pustylnik. On strictly singular and strictly co-singular embeddings between Banach lattices of functions. Math. Proc. Camb. Phil. Soc. 133 (2002). (In the press.) F. Cobos, A. Manzano and A. Martínez. Interpolation theory and measures related to operator ideals. Q. J. Math. (2) 50 (1999), 401{416. F. Cobos, A. Manzano, A. Martínez and P. Matos. On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals. Proc. R. Soc. Edinb. A 130 (2000), 971{989. F. Cobos, M. Cwikel and P. Matos. Best possible compactness results of Lions{Peetre type. Proc. Edinb.Math. Soc. 44 (2001), 153{172. A. A. Dmitriev. The interpolation of one-dimensional operators. Vorone·zGos. Univ. Trudy Nau·cn.-Issled. Inst. Mat. VGU Vyp. 11 Sb. Statej Funkcional. Analysis i Prilozen 11 (1973), 31{43. (In Russian.) D. E. Edmunds and H. Triebel.Functionspaces, entropynumbers anddi® erential operators(Cambridge University Press, 1996). S. Goldberg. Unbounded linear operators (McGraw-Hill, 1966). A. Grothendieck. Sur certain sous-espaces vectoriels de Lp . Can. J. Math. 6 (1954), 158{160. S. Heinrich. Closed operator ideals and interpolation. J. Funct. Analysis 35 (1980), 397{411. J. L. Lions and J. Peetre. Sur une classe d’ espaces d’interpolation. Inst. Hautes Etudes Sci. Publ. Math. 19 (1964), 5{68. A. Pelczy¶nski. On strictly singular and strictly co-singular operators. I and II. Bull. Acad. Polon. Sci. S¶er. Sci. Math. Astronom. Phys. 13 (1965), 31{36; 37{41. A. Pietsch. Operator ideals (Amsterdam: North-Holland, 1980). E. Pustylnik. On optimal interpolation and some interpolation properties of Orlicz spaces.Sov.Math. Dokl. 27 (1983), 333{336. E. Pustylnik. Embedding functions and their role in interpolation theory. Abstract Appl. Analysis 1 (1996), 305{325. W. Rudin. Functional analysis (McGraw-Hill, 1973). I. Singer. Bases inBanach spaces, I (Springer, 1970). I. Singer. Bases inBanach spaces, II (Springer, 1981). H. Triebel. Interpolationtheory, functionspaces, di® erential operators (Amsterdam: North-Holland, 1978).
dc.identifier.doi10.1017/S0308210500001645
dc.identifier.issn0308-2105
dc.identifier.officialurlhttp://journals.cambridge.org/download.php?file=%2FPRM%2FPRM132_02%2FS0308210500001645a.pdf&code=4cbb92
dc.identifier.relatedurlhttp://www.cambridge.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57223
dc.issue.numberPart 2
dc.journal.titleProceedings of the Royal Society of Edinburgh: Section A Mathematics
dc.language.isoeng
dc.page.final328
dc.page.initial317
dc.publisherCambridge University Press
dc.relation.projectIDPB97-0254
dc.rights.accessRightsrestricted access
dc.subject.cdu517.98
dc.subject.keywordReal Interpolation
dc.subject.keywordCompact Operators
dc.subject.keywordOperator Ideal
dc.subject.keywordMathematics
dc.subject.keywordApplied
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleSome Interpolation Results that are the Exclusive Property of Compact Operators
dc.typejournal article
dc.volume.number132
dspace.entity.typePublication
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