Homogeneous orthogonally additive polynomials on Banach Lattices
The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonally additive polynomials. It is shown that in certain la...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
John Wiley and Sons Ltd
2006
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 05873caa a22005897a 4500 | ||
|---|---|---|---|
| 001 | PAPER-7152 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203653.0 | ||
| 008 | 190411s2006 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-33744913059 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Benyamini, Y. | |
| 245 | 1 | 0 | |a Homogeneous orthogonally additive polynomials on Banach Lattices |
| 260 | |b John Wiley and Sons Ltd |c 2006 | ||
| 270 | 1 | 0 | |m Benyamini, Y.; Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel; email: yoavb@tx.technion.ac.il |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Aron, R., Boyd, C., Ryan, R., Zalduendo, I., Zeros of polynomials on Banach spaces: The real story (2003) Positivity, 7, pp. 285-295 | ||
| 504 | |a Aron, R., Gonzalo, R., Zagorodnyuk, A., Zeros of real polynomials (2000) Linear and Multi-linear Algebra, 48, pp. 107-115 | ||
| 504 | |a Carne, T.K., Cole, B., Gamelin, T.W., A uniform algebra of analytic functions on a Banach space (1989) Trans. Amer. Math. Soc., 314, pp. 639-659 | ||
| 504 | |a Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces, , Springer Monogr. Math. (Springer) | ||
| 504 | |a Drewnowski, L., Orlicz, W., On representation of orthogonally additive functionals (1969) Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 17, pp. 167-173 | ||
| 504 | |a Friedman, N., Katz, M., Additive functionals on Lp spaces (1966) Canad. J. Math, 18, pp. 1264-1271 | ||
| 504 | |a Garrido, M.I., Jaramillo, J.A., Llavona, J.G., Polynomial topologies on a Banach space (2005) Topology Appl., 153, pp. 854-867 | ||
| 504 | |a Kalton, N.J., Peck, N.T., Roberts, J.W., (1984) An F-space Sampler, , Cambridge University Press | ||
| 504 | |a Lassalle, S., Llavona, J.G., Weak-polynomial convergence on spaces ℓp and Lp (2004) Positivity, 8, pp. 283-296 | ||
| 504 | |a Lindenstrauss, J., Tzafriri, L., (1977) Classical Banach Spaces II, , Springer | ||
| 504 | |a Marcus, M., Mizel, V.J., Representation theorems for nonlinear disjointly additive functionals and operators on Sobolev spaces (1977) Trans. Amer. Math. Soc., 228, pp. 1-45 | ||
| 504 | |a Mizel, V.J., Sundaresan, K., Representation of vector valued nonlinear functions (1971) Trans. Amer. Math. Soc., 159, pp. 111-127 | ||
| 504 | |a Mujica, J., (1986) Complex Analysis in Banach Spaces, , Math. Studies 120 (North-Holland, Amsterdam) | ||
| 504 | |a Natanson, I.P., (1960) Theory of Functions of a Real Variable, 2. , Frederick Ungar Publishing Co., New York | ||
| 504 | |a PeŁczyński, A., On weakly compact polynomial operators on B-spaces with Dunford-Pettis property (1963) Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 11, pp. 371-378 | ||
| 504 | |a PeŁczyński, A., A theorem of Dunford-Pettis type for polynomial operators (1963) Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 11, pp. 379-386 | ||
| 504 | |a Pérez-García, D., Villanueva, I., Orthogonally additive polynomials on spaces of continuous functions (2005) J. Math. Anal. Appl., 306, pp. 97-105 | ||
| 504 | |a Pinsker, A.G., Sur une fonctionnelle dans l'espace de Hilbert (1938) Dokl. Acad. USSR (N.S.), 20, pp. 411-414 | ||
| 504 | |a Rudin, W., (1973) Functional Analysis, , McGraw-Hill | ||
| 504 | |a Sundaresan, K., Geometry of spaces of homogeneous polynomials on Banach lattices (1991) Applied Geometry and Discrete Mathematics, 4, pp. 571-586. , DIMACS Ser. Discrete Math. Theoret. Comput. Sci. (Amer. Math. Soc., Providence, RI) | ||
| 520 | 3 | |a The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonally additive polynomials. It is shown that in certain lattices every element can be represented as the sum of two or three zeros or, at least, can be approximated by such sums. It is also indicated how these results can be used to study weak topologies induced by orthogonally additive polynomials on Banach lattices. © 2006 London Mathematical Society. |l eng | |
| 536 | |a Detalles de la financiación: Secretaría de Ciencia y Técnica, Universidad de Buenos Aires, BFM2000-0609, PICT03-15033, X108 | ||
| 536 | |a Detalles de la financiación: The research of the first author was supported by the Technion Fund for the Promotion of Research, the second author was partially supported by UBACyT X108 and PICT03-15033, and the third author was supported in part by Project BFM2000-0609. | ||
| 593 | |a Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel | ||
| 593 | |a Departamento de Matemática - PAB I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina | ||
| 593 | |a Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain | ||
| 700 | 1 | |a Lassalle, S. | |
| 700 | 1 | |a Llavona, J.G. | |
| 773 | 0 | |d John Wiley and Sons Ltd, 2006 |g v. 38 |h pp. 459-469 |k n. 3 |p Bull. Lond. Math. Soc. |x 00246093 |w (AR-BaUEN)CENRE-300 |t Bulletin of the London Mathematical Society | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-33744913059&doi=10.1112%2fS0024609306018364&partnerID=40&md5=ee35aa6cb26046703514bf0b3a598d2c |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1112/S0024609306018364 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00246093_v38_n3_p459_Benyamini |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246093_v38_n3_p459_Benyamini |y Registro en la Biblioteca Digital |
| 961 | |a paper_00246093_v38_n3_p459_Benyamini |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 68105 | ||