On the Primariness of the Banach Space l ∞ /C 0

Set theoretical aspects of the Banach space l∞/c0

“…The main purpose of this paper is to present two statements of this kind. The points at issue of our considerations are questions posed by Drewnowski and Roberts in [4]. Before we present a short sketch of their results, let us recall some facts and standard deÿnitions.…”

PFA and complemented subspaces of ℓ∞/c0

“…Our paper is motivated by the question (Drewnowski and Roberts [3], Leonard and Whitfield [6]) of whether or not C(N * ) is primary. A Banach space X is primary if whenever X is written as the sum A ⊕ B of complemented subspaces, then one of A, B is isomorphic to X .…”

“…Negrepontis [8,Corollary 3.2] showed that CH implies that the closure Y of a non-compact cozero subset of N * is a retract of N * , and, therefore, there is a norm bounded linear lifting of the Banach space C(Y) to a complemented subset of C(N * ). Later, Drewnowski and Roberts [3] established that the existence of such a lifting implied that C(N * ) is primary. It is already known to be consistent that there is no such lifting; an even stronger result was shown to hold in the Cohen model in Brech and Koszmider [1].…”

The space (𝑙_{∞}/𝑐₀,𝑤𝑒𝑎𝑘) is not a Radon space

“…Following that proof and the work of Drewnowski and Roberts [ 1 ], this paper is devoted to proving that the classical space (I^/Cq , weak) is not a Radon space. Note that this fact could be proved if Z were a subspace of /^ /c0 , but this is not yet known.…”