[Scissions d'extensions et bidimension homologique de l'algèbre d'opérateurs bornés sur un espace de Banach]
Nous démontrons qu'il existe un espace de Banach tel que :
- • l'algèbre de Banach des opérateurs linéaires bornés sur E a une extension singulière, qui scinde algébriquement, mais qui ne scinde pas fortement ;
- • la bidimension homologique de est au moins deux.
We show that there exists a Banach space E such that:
- • the Banach algebra of bounded, linear operators on E has a singular extension that splits algebraically, but it does not split strongly;
- • the homological bidimension of is at least two.
Accepté le :
Publié le :
Niels Jakob Laustsen 1 ; Richard Skillicorn 1
@article{CRMATH_2016__354_5_459_0, author = {Niels Jakob Laustsen and Richard Skillicorn}, title = {Splittings of extensions and homological bidimension of the algebra of bounded operators on a {Banach} space}, journal = {Comptes Rendus. Math\'ematique}, pages = {459--463}, publisher = {Elsevier}, volume = {354}, number = {5}, year = {2016}, doi = {10.1016/j.crma.2015.12.020}, language = {en}, }
TY - JOUR AU - Niels Jakob Laustsen AU - Richard Skillicorn TI - Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space JO - Comptes Rendus. Mathématique PY - 2016 SP - 459 EP - 463 VL - 354 IS - 5 PB - Elsevier DO - 10.1016/j.crma.2015.12.020 LA - en ID - CRMATH_2016__354_5_459_0 ER -
%0 Journal Article %A Niels Jakob Laustsen %A Richard Skillicorn %T Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space %J Comptes Rendus. Mathématique %D 2016 %P 459-463 %V 354 %N 5 %I Elsevier %R 10.1016/j.crma.2015.12.020 %G en %F CRMATH_2016__354_5_459_0
Niels Jakob Laustsen; Richard Skillicorn. Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 459-463. doi : 10.1016/j.crma.2015.12.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.020/
[1] Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc., Volume 137 (1999)
[2] Homomorphisms and derivations from , J. Funct. Anal., Volume 120 (1994), pp. 201-219
[3] The Homology of Banach and Topological Algebras, Kluwer, Dordrecht, The Netherlands, 1989
[4] 31 problems of the homology of the algebras of analysis, Linear Complex Analysis Problem Book III, Part I, Lect. Notes Math., vol. 1573, Springer-Verlag, 1994, pp. 54-78
[5] Continuity of homomorphisms of algebras of operators, J. Lond. Math. Soc. (2), Volume 42 (1967), pp. 537-541
[6] The Wedderburn decomposition of Banach algebras with finite dimensional radical, Amer. J. Math., Volume 90 (1968), pp. 866-876
[7] Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Camb. Philos. Soc., Volume 120 (1996), pp. 455-473
[8] Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations (submitted) | arXiv
[9] Discontinuous derivations on the algebra of bounded operators on a Banach space, J. Lond. Math. Soc. (2), Volume 40 (1989), pp. 305-326
Cité par Sources :
Commentaires - Politique