Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces.
| dc.contributor.author | Jiménez Sevilla, María Del Mar | |
| dc.contributor.author | Payá Albert, Rafael | |
| dc.date.accessioned | 2023-06-20T18:48:15Z | |
| dc.date.available | 2023-06-20T18:48:15Z | |
| dc.date.issued | 1998 | |
| dc.description.abstract | For each natural number N, we give an example of a Banach space X such that the set of norm attaining N{linear forms is dense in the space of all continuous N{linear forms on X, but there are continuous (N +1){linear forms on X which cannot be approximated by norm attaining (N+1){linear forms. Actually, X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22372 | |
| dc.identifier.issn | 0039-3223 | |
| dc.identifier.officialurl | https://eudml.org/doc/216467 | |
| dc.identifier.relatedurl | https://eudml.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58665 | |
| dc.issue.number | 2 | |
| dc.journal.title | Studia Mathematica | |
| dc.language.iso | eng | |
| dc.page.final | 112 | |
| dc.page.initial | 99 | |
| dc.publisher | Polish Acad Sciencies Inst Mathematics | |
| dc.relation.projectID | PB 93-0452 | |
| dc.relation.projectID | PB 93-1142 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Norm attaining multilinear forms and polynomials | |
| dc.subject.keyword | weakly continuous multilinear forms and polynomials | |
| dc.subject.keyword | Lorentz sequence spaces. | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces. | |
| dc.type | journal article | |
| dc.volume.number | 127 | |
| dcterms.references | M. D. Acosta, F. J. Aguirre and R. Pay�a, There is no bilinear Bishop-Phelps Theorem, to appear in Israel J. Math. M. D. Acosta, F. J. Aguirre and R. Pay�a, A space by W. Gowers and new results on norm and numerical radius attaining operators, Acta Univ. Carolinae, Math. et Phys. 33 (1992), 5-14. F. J. Aguirre, Algunos problemas de optimizaci�on en dimensi�on in�nita: aplicaciones lineales y multilineales que alcanzan su norma, Tesis Doctoral, Universidad de Granada, 1995. R. Aron, C. Finet and E. Werner, Some remarks on norm attaining N-linear forms, In: Functions spaces (K. Jarosz, Ed.) Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, New York 1995, pp. 19-28. Z. Altshuler, P. G. Casazza and B. L. Lin, On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math. 15 (1973), 140-155. E. R. Bishop and R. Phelps, A proof that every Banach space is subre exive, Bull. Amer. Math. Soc. 67 (1961), 97-98. P.G. Casazza and Bor{Luh Lin, On symmetric sequences in Lorentz sequence spaces II, Israel J. Math. 17 (1974), 191-218. Y.-S. Choi, Norm attaining bilinear forms on L1[0; 1] , preprint. Yun Sung Choi and Sung Guen Kim, Norm or numerical radius attaining multilinear mappings and polynomials, to appear in J. London Math. Soc. V. Dimant and S. Dineen, Banach subspaces of spaces of holomorphic functions and related topics, preprint. V. Dimant and I. Zalduendo, Bases in spaces of multilinear forms over Banach spaces, to appear in the J. Funct. Anal. and Appl. D. J. H. Garling, On Symmetric sequences spaces, Proc. London Math. Soc. 16 (1966), 85-106. R. Gonzalo and J. A. Jaramillo, Compact polynomials between Banach spaces, Extracta Math. 8 (1993), 42-48. W. Gowers, Symmetric block bases of sequences with large average growth, Israel J. Math. 69 (1990), 129-149. P. Harmand, D. Werner and W. Werner, M-Ideals in Banach spaces and Banach algebras, L.N.M. 1547, Springer-Verlag, Berlin 1993. H. Knaust, Orlicz sequence spaces of Banach{Saks type, Arch. Math. 59 (1992), 562-565. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer-Verlag, 1977. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Springer-Verlag, 1979. S. Reisner, A factorization theorem in Banach lattices and its applications to Lorentz spaces, Ann. Inst. Fourier, Grenoble 31, 1 (1981), 239-255. W. L. C. Sargent, Some sequences spaces related to the `p spaces , J. London Math. Soc. 35 (1960), 161-171. A. E. Tong, Diagonal submatrices of matrix maps, Paci�c J. Math. 32 (1970), 551-559. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 | |
| relation.isAuthorOfPublication.latestForDiscovery | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 |
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