Extension of bilinear forms on Banach spaces
| dc.contributor.author | Castillo, Jesús M.F. | |
| dc.contributor.author | García, R. | |
| dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
| dc.date.accessioned | 2023-06-20T16:59:26Z | |
| dc.date.available | 2023-06-20T16:59:26Z | |
| dc.date.issued | 2001 | |
| dc.description.abstract | We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E --> X is said to be (linearly) N-exact if N-linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide. | |
| 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/16650 | |
| dc.identifier.doi | http://dox.doi.org/10.1090/S0002-9939-01-05986-X | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.officialurl | http://www.ams.org/journals/proc/2001-129-12/S0002-9939-01-05986-X/S0002-9939-01-05986-X.pdf | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57581 | |
| dc.issue.number | 12 | |
| dc.journal.title | Proceedings of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 3656 | |
| dc.page.initial | 3647 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | PB97-0377; PB96-0607 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Bilinear forms | |
| dc.subject.keyword | tensor product | |
| dc.subject.keyword | cotype-2 space | |
| dc.subject.keyword | embedding | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Extension of bilinear forms on Banach spaces | |
| dc.type | journal article | |
| dc.volume.number | 129 | |
| dcterms.references | R. Aron and P. Berner, A Hahn-Banach extension theorem for analytic mapping, Bull. Soc. Math. France 106 (1978), 3-24. MR 80e:46029 F. Blasco, Complementation in spaces of symmetric tensor products and polynomials, Studia Math. 123 (1997), 165-173. MR 98d:46043 J. Bourgain, New classes of Lp-spaces, Lecture Notes in Mathematics 889, Springer, Berlin and New York, 1991. MR 83j:46028 F. Cabello S anchez, J.M.F. Castillo and R. Garc ia, Polynomials on dual isomorphic spaces, Ark. Mat. 38 (2000), 37-44. CMP 2000:11 F. Cabello S anchez, R. Garc ia and I. Villanueva, Extension of multilinear operators on Banach spaces, Extracta Math. 15 (2000), 291-334. D. Carando, Extendible polynomials on Banach spaces, J. Math. Anal. and Appl. 233 (1999), 359-372. MR 2000d:46057 D. Carando and I. Zalduendo, A Hahn-Banach theorem for integral polynomials, Proc. Amer. Math. Soc. 127 (1999), 241-250. MR 99b:46067 J.M.F. Castillo and M. Gonz ales, Three-space problems in Banach space theory, Lecture Notes in Mathematics 1667, Springer 1997. MR 99a:46034 A. Defant and K. Floret, Tensor norms and Operator ideals, North-Holland Math. Stud., 176, 1993. MR 94e:46130 S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud., 57, 1981. MR 84b:46050 S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monographs in Math., Springer, 1999. CMP 99:17 J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge Tracts in Mathematics 43, Cambridge Univ. Press. 1995. MR 96i:46001 P. Galindo, D. Garc ia, M. Maestre and J. Mujica, Extension of multilinear mappings on Banach spaces, Studia Math. 108 (1994), 55-76. MR 95f:46072 E. Hilton and K. Stammbach, A course in homological algebra, Graduate Texts in Mathematics 4, Springer-Verlag. MR 97k:18001 H. Jarchow, On Hilbert-Schmidt spaces, Rendiconti CircoloMat. di Palermo (Suppl.) II (1982), 153-160. MR 84d:46017 N. Kalton, Locally complemented subspaces and Lp-spaces for 0 < p < 1, Math. Nachr. 115 (1984), 71-97. MR 86h:46006 N. Kalton and N.T. Peck, Twisted sums of sequence spaces and the three-space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30. MR 82g:46021 P. Kirwan and R. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proc. Amer. Math. Soc. 126 (1998), 1023-1029. MR 98f:46042 J. Lindenstrauss, On a certain subspace of l1, Bull. Polish Acad. Sci. 12 (1964), 539-542. MR 30:5153 J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Sequence spaces, Springer, 1977. MR 58:17766 G. Pisier, Counterexamples to a conjecture of Grothendieck, Acta Mat. (1983), 181-208. MR 85m:46017 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 3656 J. M. F. CASTILLO, R. GARC IA, AND J. A. JARAMILLO R. Ryan, Dunford-Pettis properties, Bull. Polish Acad. Sci. 27 (1979), 373-379. MR 80m:46018 I. Zalduendo, Extending polynomials - a survey, Pub. Dept. An al. Mat. Univ. Complutense Madrid, 41. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b6e753b-df15-44ff-8042-74de90b4e3e9 |
Download
Original bundle
1 - 1 of 1