1-complemented subspaces of Banach spaces of universal disposition

Abstract

We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\aleph$-injectivity --- in the notion of $(\alpha ,\beta )$-injectivity ($(\alpha ,\beta {)}_{\lambda }$-injectivity if the parameter $\lambda$ has to be specified). Then, extend the notion of space of universal disposition to space of universal $(\alpha ,\beta )$-disposition. Finally, we characterize the $1$-complemented subspaces of spaces of universal $(\alpha ,\beta )$-disposition as precisely the spaces $(\alpha ,\beta {)}_1$-injective.

References in corpus (2)

• Banach spaces of universal disposition
• Quasi-Banach spaces of almost universal disposition