[Un espace failble de Hilbert avec peu de symétries]
Nous construisons un space de Banach qui est un espace failble de Hilbert et n'admettant aucune sous-espace bloc isomorphe linéaire à une sous-espace. Nous démontrons les propriétés de par démontrons que est fortement asymptotique et tout opérateur borné de soit une variation strictment singulière d'un opérateur diagonal par rappert à la base.
We construct a separable Banach space with an unconditional basis that is a weak Hilbert space and no block subspace is linearly isomorphic to any of its proper subspaces. We prove that the space satisfies these properties by showing it is strongly asymptotic and that every bounded linear operator on is a strictly singular perturbation of a diagonal operator with respect to the unit vector basis.
Accepté le :
Publié le :
Spiros A. Argyros 1 ; Kevin Beanland 2 ; Theocharis Raikoftsalis 1
@article{CRMATH_2010__348_23-24_1293_0, author = {Spiros A. Argyros and Kevin Beanland and Theocharis Raikoftsalis}, title = {A weak {Hilbert} space with few symmetries}, journal = {Comptes Rendus. Math\'ematique}, pages = {1293--1296}, publisher = {Elsevier}, volume = {348}, number = {23-24}, year = {2010}, doi = {10.1016/j.crma.2010.10.032}, language = {en}, }
TY - JOUR AU - Spiros A. Argyros AU - Kevin Beanland AU - Theocharis Raikoftsalis TI - A weak Hilbert space with few symmetries JO - Comptes Rendus. Mathématique PY - 2010 SP - 1293 EP - 1296 VL - 348 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2010.10.032 LA - en ID - CRMATH_2010__348_23-24_1293_0 ER -
Spiros A. Argyros; Kevin Beanland; Theocharis Raikoftsalis. A weak Hilbert space with few symmetries. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1293-1296. doi : 10.1016/j.crma.2010.10.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.032/
[1] Complexity of weakly null sequences, Dissertationes Math. (Rozprawy Mat.), Volume 321 (1992), p. 44
[2] A hereditarily indecomposable asymptotic Banach space, Glasg. Math. J., Volume 48 (2006) no. 3, pp. 503-532
[3] Ramsey Methods in Analysis, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser Verlag, Basel, 2005
[4] Asymptotic hereditarily indecomposable Banach spaces, Illinois J. Math., Volume 51 (2007) no. 3, pp. 767-803
[5] On strongly asymptotic spaces and minimality, J. Lond. Math. Soc. (2), Volume 75 (2007) no. 2, pp. 409-419
[6] Banach spaces without minimal subspaces, J. Funct. Anal., Volume 257 (2009) no. 1, pp. 149-193
[7] Banach spaces with small spaces of operators, Math. Ann., Volume 307 (1997) no. 4, pp. 543-568
[8] A reflexive Banach space which is not sufficiently Euclidean, Studia Math., Volume 55 (1976) no. 2, pp. 201-205
[9] Banach lattices with property (H) and weak Hilbert spaces, Illinois J. Math., Volume 36 (1992) no. 3, pp. 345-371
[10] Weak Hilbert spaces, Proc. London Math. Soc. (3), Volume 56 (1988) no. 3, pp. 547-579
[11] The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989
[12] On the existence of asymptotic- structures in Banach spaces, Canad. Math. Bull., Volume 50 (2007) no. 4, pp. 619-631
Cité par Sources :
Commentaires - Politique