Banach spaces whose algebras of operators have a large group of unitary elements

• Autores: Julio Becerra Guerrero , María Burgos , El Amin Kaidi Lhachmi , Ángel Rodríguez Palacios
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 144, Nº 1, 2008, págs. 97-108
• Idioma: inglés
• DOI: 10.1017/s0305004107000655
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• Resumen

  • We prove that a complex Banach space X is a Hilbert space if (and only if) the Banach algebra (of all bounded linear operator on X) is unitary and there exists a conjugate-linear algebra involution ¿ on satisfying T¿ = T-1 for every surjective linear isometry T on X. Appropriate variants for real spaces of the result just quoted are also proven. Moreover, we show that a real Banach space X is a Hilbert space if and only if it is a real JB*-triple and is -unitary, where stands for the dual weak-operator topology