This is an announcement for the paper “1-complemented subspaces of Banach spaces of universal disposition” by Jesús M. F. Castillohttps://arxiv.org/find/math/1/au:+Castillo_J/0/1/0/all/0/1, Yolanda Morenohttps://arxiv.org/find/math/1/au:+Moreno_Y/0/1/0/all/0/1.
Abstract: We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\mathcal{N}$-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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.03823