On strong M-bases in Banach spaces with PRI

• Autores: Deba P. Sinha
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 51, Fasc. 3, 2000, págs. 277-284
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • If every member of a class $\mathcal{P}$ of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class $\mathcal{P}$, then it is proved that every Banach space in $\mathcal{P}$ has a strong $M$-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an $M$-basis such that the dual unit ball is weak$^\ast$ angelic and every $\mathcal{C}(K)$ space for a Valdivia compact set $K$, has a strong $M$-basis.

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