Weak-Polynomial Convergence on a Banach Space
| dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
| dc.contributor.author | Prieto Yerro, M. Ángeles | |
| dc.date.accessioned | 2023-06-20T17:00:31Z | |
| dc.date.available | 2023-06-20T17:00:31Z | |
| dc.date.issued | 1993-06 | |
| dc.description.abstract | We show that any super-reflexive Banach space is a LAMBDA-space (i.e., the weak-polynomial convergence for sequences implies the norm convergence). We introduce the notion Of kappa-space (i.e., a Banach space where the weak-polynomial convergence for sequences is different from the weak convergence) and we prove that if a dual Banach space Z is a kappa-space with the approximation property, then the uniform algebra A(B) on the unit ball of Z generated by the weak-star continuous polynomials is not tight. | |
| 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/16788 | |
| dc.identifier.doi | 10.2307/2160323 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57615 | |
| dc.issue.number | 2 | |
| dc.journal.title | Proceedings of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 468 | |
| dc.page.initial | 463 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | PB 87-1031 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.518.235 | |
| dc.subject.keyword | Tight algebras | |
| dc.subject.keyword | super-reflexive Banach space | |
| dc.subject.keyword | equivalent uniformly convex norm | |
| dc.subject.keyword | -space | |
| dc.subject.keyword | weak-polynomial convergence for sequences implies the norm convergence | |
| dc.subject.keyword | weak polynomial convergence for sequences is different from the weakconvergence | |
| dc.subject.keyword | dual Banach space | |
| dc.subject.keyword | approximation property | |
| dc.subject.keyword | uniform algebra | |
| dc.subject.keyword | not weakly compact Hankel-type operator | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Weak-Polynomial Convergence on a Banach Space | |
| dc.type | journal article | |
| dc.volume.number | 118 | |
| dcterms.references | R. Alencar, R. Aron, and S. Dineen, A reflexive space of holomorphic functions in infinite many variables, Proc. Amer. Math. Soc. 90 (1984), 407-411. R. Aron and C. Herves, Weakly sequentially continuous analytic functions on a Banach space, Functional Analysis, Holomorphy and Approximation Theory II (G. Zapata, ed.), North-Holland, Amsterdam, 1984, pp. 23-38. T. Carne, B. Cole, and T. Gamelin, A uniform algebra of analytic functions on a Banach space, Trans. Amer. Math. Soc. 314 (1989), 639-659. P. G. Casazza and T. J. Shura, Tsirelson space, Lecture Notes in Math., vol. 1363, Springer-Verlag, Berlin and New York, 1980. J. F. Castillo and C. Sanchez, Weakly-p-compact, p-Banach-Saks and super-reflexive Banach spaces, preprint. S. B. Chae, Holomorphy and calculus in normed spaces, Marcel Dekker, New York, 1985. M. Day, Normed linear spaces, Springer-Verlag, Berlin and New York, 1973. J. Diestel, Geometry of Banach spaces, Lecture Notes in Math., vol. 485, Springer-Verlag, Berlin and New York, 1975. __, Sequences and series in Banach spaces, Graduate Texts in Math., vol. 92, Springer-Verlag, Berlin and New York, 1984. T. W. Gamelin, Uniform algebras, Chelsea, New York, 1984. J. Globevnik, On interpolation by analytic maps in infinite dimensions, Math. Proc. Cambridge Philos. Soc. 83 (1978), 243-254. R. James, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409-420. W. Johnson, On finite dimensional subspaces of Banach spaces with local unconditional structure, Studia Math. 51 (1974), 226-240. B. Maurey and G. Pisier, Series de variables aleatories vectorielles independantes et proprieties geometriques des espaces de Banach, Studia Math. 58 (1976), 45-90. R. Ryan, Dunford-Pettisp roperties,B ull. Polon. Acad. Sci. 27 (1979), 373-379. D. Van Dulst, Reflexive and super-reflexive spaces, Math. Centre Tracts, vol. 102, North-Holland, Amsterdam, 1982. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
| relation.isAuthorOfPublication | f2a43f90-b551-412e-a95d-2587bbfaa27d | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b6e753b-df15-44ff-8042-74de90b4e3e9 |
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