New York Journal of Mathematics
Volume 24 (2018) 251-260


Jesús M.F. Castillo, Yolanda Moreno, and Marilda A. Simões

1-complemented subspaces of Banach spaces of universal disposition

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Published: March 1, 2018
Keywords: Separable injectivity, universal separable injectivity, universal disposition, local injectivity, 1-complemented subspaces
Subject: 46B03, 46M40

We first unify all notions of partial injectivity appearing in the literature -- (universal) separable injectivity, (universal) א-injectivity -- in the notion of (α, β)-injectivity ((α, β)λ-injectivity if the parameter λ has to be specified). Then, extend the notion of space of universal disposition to space of universal (α, β)-disposition. Finally, we characterize the 1-complemented subspaces of spaces of universal (α, β)-disposition as precisely the spaces (α, β)1-injective.


The research of the two first authors has been supported in part by project MTM2016-76958-C2-1-P and Project IB16056 and Ayuda a Grupos GR15152 de la Junta de Extremadura.

Author information

Jesús M.F. Castillo:
Departamento de Matematicas, Universidad de Extremadura, 06071 Badajoz, España

Yolanda Moreno:
Departamento de Matematicas, Escuela Politécnica, Universidad de Extremadura, 10003 Cáceres, España

Marilda A. Simões:
Dipartimento di Matematica "G. Castelnuovo", Universitá di Roma "La Sapienza", P.le A. Moro 2, 00185 Roma, Italia