5 papers
Unconditional basic sequences in spaces of large density
Pandelis Dodos, Jordi Lopez Abad, Stevo Todorcevic
We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement…
The oscillation stability problem for the Urysohn sphere: A combinatorial approach
Jordi Lopez Abad, Lionel Nguyen Van Thé
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for in the context of the Urysohn space $\Ur$. In particular, we sho…
A -saturated Banach space with no long unconditional basic sequences
Jordi Lopez Abad, Stevo Todorcevic
We present a Banach space with a Schauder basis of length which is saturated by copies of and such that for every closed decomposition of a closed subsp…
Canonical equivalence relations on nets of
Jordi Lopez Abad
We give a list of canonical equivalence relations on discrete nets of the positive unit sphere of . This generalizes results of W. T. Gowers and A. D. Taylor.
A classification of Tsirelson type spaces
Jordi Lopez Abad, Antonis Manoussakis
We give a complete classification of mixed Tsirelson spaces T[(F\_i, theta\_i)\_{i=1}^r ] for finitely many pairs of given compact and hereditary families F\_i of finite sets of in…