Unital Banach algebras and their subalgebras

• Autores: Miao Tianxuan
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 2, 2007, págs. 343-347
• Idioma: inglés
• DOI: 10.1017/s0305004107000266
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let A be a Banach algebra with a bounded approximate identity. We prove that if A is not unital, then there is a nonunital subalgebra B of A with a sequential bounded approximate identity. It follows that A must be unital if A is weakly sequentially complete and B** under the first Arens multiplication has a unique right identity for every subalgebra B of A with a sequential bounded approximate identity. As a consequence, we prove a result of Ülger that if A is both weakly sequentially complete and Arens regular, then A must be unital.