Motivated by the Lipschitz-lifting property of Banach spaces introduced Godefroy and Kalton, we consider lattice-lifting property, which is an analogous notion within category lattices lattice homomorphisms. Namely, a X satisfies if every homomorphism to having bounded linear right-inverse must have right-inverse. In terms free lattices, this can be rephrased into following question: embed they...

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms weakly null nets, we introduce unbounded operators replacing weak convergence with absolutely (uaw-convergence) lattices. We characterize order lattices and reflexive these operators. Moreover, motivated characterizing lattice Cauchy sequences, consider pre-unbounded which maps uaw-Cauchy sequences to...

In this paper we investigate a property named GL(p, q) which is closely related to the Gordon-Lewis property. Our results on GL(p, q) are then used to estimate volume ratios relative to lp, 1 < p ≤ ∞, of unconditional direct sums of Banach spaces. Introduction In this paper we investigate a property named GL(p, q), 1 ≤ p ≤ ∞, 1 ≤ q ≤ ∞, closely related to the Gordon-Lewis property GL, and the b...

An element s of an (abstract) algebra A is a single element of A if asb = 0 and a, b ∈ A imply that as = 0 or sb = 0. Let X be a real or complex reflexive Banach space, and let B be a finite atomic Boolean subspace lattice on X, with the property that the vector sum K +L is closed, for every K,L ∈ B. For any subspace lattice D ⊆ B the single elements of Alg D are characterised in terms of a coo...

A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. A c0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l2 is constructed. A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. In [2] and [3], it was asked whether all quotient spaces ...