Abstract:
We show that if E is a real Banach space such that E′ has the approximation property and such that ℓ1 → ⊗ n,s,e,E, then the set of extreme points of the unit ball of PI (nE) is equal to {± Φn: Φ ∈ E′ ∥ Φ ∥ = 1}. Under the additional assumption that E′ has a countable norming set, we see that the set of exposed points of the unit ball of PI(nE) is also equal to {± Φn Φisin; E′ ∥ Φ ∥ © 2009 American Mathematical Society.
Registro:
Documento: |
Artículo
|
Título: | Extreme and exposed points of spaces of integral polynomials |
Autor: | Boyd, C.; Lassalle, S. |
Filiación: | School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland Departamento de Matemática, Pab. i - Cuidad Universitaria (FCEN), Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
|
Palabras clave: | Exposed points; Extreme points; Integral polynomials |
Año: | 2010
|
Volumen: | 138
|
Número: | 4
|
Página de inicio: | 1415
|
Página de fin: | 1420
|
DOI: |
http://dx.doi.org/10.1090/S0002-9939-09-10158-2 |
Título revista: | Proceedings of the American Mathematical Society
|
Título revista abreviado: | Proc. Am. Math. Soc.
|
ISSN: | 00029939
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n4_p1415_Boyd |
Referencias:
- Acosta, M., Becerra Guerrero, J., Slices in the unit ball of the symmetric tensor product of C(K) and L1 (μ) (2009) Ark. Mat., 47 (1), pp. 1-12. , MR2480913
- Acosta, M., Becerra Guerrero, J., Slices in the unit ball of the symmetric tensor product of a Banach space J. Convex Anal., , to appear
- Boyd, C., Ryan, R.A., Geometric Theory of Spaces of Integral Polynomials and Symmetric Tensor Products (2001) Journal of Functional Analysis, 179 (1), pp. 18-42. , DOI 10.1006/jfan.2000.3666, PII S0022123600936668
- Carando, D., Dimant, V., Duality in spaces of nuclear and integral polynomials (2000) J.Math.Anal. Appl., 241, pp. 107-121. , MR1738337 (2001c:46089)
- Carando, D., Zalduendo, I., A Hahn-Banach theorem for integral polynomials (1999) Proc.Amer. Math. Soc., 127, pp. 241-250. , MR1458865 (99b:46067)
- Dineen, S., Holomorphy types on a Banach space (1971) Studia Math., 39, pp. 241-288. , MR0304705 (46:3837)
- Dineen, S., Complex analysis on infinite-dimensional spaces (1999) Monographs in Mathematics, , Springer-Verlag London MR1705327 (2001a:46043)
- Dineen, S., Extreme integral polynomials on a complex Banach space (2003) Mathematica Scandinavica, 92 (1), pp. 129-140
- Jarchow, H., (1981) Locally Convex Spaces, , B.G. Teubner, Stuttgart. MR632257 (83h:46008)
- Kirwan, P., Ryan, R.A., Extendibility of homogeneous polynomials on Banach spaces (1998) Proceedings of the American Mathematical Society, 126 (4), pp. 1023-1029
- Ruess, W.M., Stegall, C.P., Extreme points in duals of operator spaces (1982) Math. Ann., 261, pp. 535-546. , MR682665 (84e:46007)
- Ruess, W.M., Stegall, C.P., Exposed and denting points in duals of operator spaces (1986) Israel J. Math., 53, pp. 163-190. , MR845870 (87j:46015)
- Ryan, R.A., Turett, B., Geometry of Spaces of Polynomials (1998) Journal of Mathematical Analysis and Applications, 221 (2), pp. 698-711. , DOI 10.1006/jmaa.1998.5942, PII S0022247X9895942X
Citas:
---------- APA ----------
Boyd, C. & Lassalle, S.
(2010)
. Extreme and exposed points of spaces of integral polynomials. Proceedings of the American Mathematical Society, 138(4), 1415-1420.
http://dx.doi.org/10.1090/S0002-9939-09-10158-2---------- CHICAGO ----------
Boyd, C., Lassalle, S.
"Extreme and exposed points of spaces of integral polynomials"
. Proceedings of the American Mathematical Society 138, no. 4
(2010) : 1415-1420.
http://dx.doi.org/10.1090/S0002-9939-09-10158-2---------- MLA ----------
Boyd, C., Lassalle, S.
"Extreme and exposed points of spaces of integral polynomials"
. Proceedings of the American Mathematical Society, vol. 138, no. 4, 2010, pp. 1415-1420.
http://dx.doi.org/10.1090/S0002-9939-09-10158-2---------- VANCOUVER ----------
Boyd, C., Lassalle, S. Extreme and exposed points of spaces of integral polynomials. Proc. Am. Math. Soc. 2010;138(4):1415-1420.
http://dx.doi.org/10.1090/S0002-9939-09-10158-2