Resumen de On strong M-bases in Banach spaces with PRI

Deba P. Sinha

• 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.