Almost isometric ideals and non-separable Gurariy spaces
Journal of Mathematical Analysis and Applications
The main result of this short note is that a (non-separable) Banach space is a Gurariy space if and only if every separable almost isometric ideal in X is isometric to the separable Gurariy space G. We also obtain a similar characterization of L1-predual spaces in terms of ideals. Along the way, we show that the family of ideals/almost isometric ideals in a Banach space is closed under increasing limits. And hence, the family of all separable ideals/almost isometric ideals in a Banach space is a skeleton.
Bandyopadhyay, Pradipta; Dutta, S.; and Sensarma, A., "Almost isometric ideals and non-separable Gurariy spaces" (2018). Journal Articles. 1369.