Transfinite (almost isometric) ideals in Banach spaces

Abstract We present and study some transfinite versions of (almost isometric) ideals in Banach spaces. As these notions are closely related with Lindenstrauss and Gurariĭ spaces respectively, we will present a similar characterization for transfinite injective spaces and spaces of (almost) universal disposition in terms of these transfinite ideals. Furthermore, we construct several examples outside these type of Banach spaces and make a revision of some classical results for transfinite ideals.