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arXiv · 1708.03823

1-complemented subspaces of Banach spaces of universal disposition

Jesús M. F. Castillo·Yolanda Moreno
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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.

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Jesús M. F. Castillo, Yolanda Moreno. 2017-08-12. 1-complemented subspaces of Banach spaces of universal disposition. https://arxiv.org/abs/1708.03823

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