Embedding Banach spaces into the space of bounded functions with countable support

Abstract

We prove that a WLD subspace of the space ℓ∞cfalse(normalΓfalse) consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into ℓ∞ if and only if it does not contain isometric copies of c0false(ω1false). Moreover, a subspace of ℓ∞cfalse(ω1false) is constructed that has an unconditional basis, does not embed into ℓ∞, and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of c0false(ω1false)).

Classifying the closed ideals of bounded operators on two families of non-separable classical Banach spaces

“…(ii) We refer to [11] for a detailed discussion of the condition in Lemma 3.1(ii) that the image of T admits an injective operator into ∞ .…”

Classifying the closed ideals of bounded operators on two families of non-separable classical Banach spaces

“…(ii) We refer to [11] for a detailed discussion of the condition in Lemma 3.1(ii) that the image of T admits an injective operator into ℓ ∞ .…”