5 papers · 1 filter
Banach-Stone-like results for combinatorial Banach spaces
Christina Brech, Claribet Piña
We show that under a certain topological assumption on two compact hereditary families $\F$ and $\G$ on some infinite cardinal , the corresponding combinatorial spaces $X_\F$ an…
Isometries of combinatorial Banach spaces
C. Brech, V. Ferenczi, A. Tcaciuc
We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show…
An isometrically universal Banach space induced by a non-universal Boolean algebra
Christina Brech, Piotr Koszmider
Given a Boolean algebra , we construct another Boolean algebra with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)…
-sums and the Banach space
Christina Brech, Piotr Koszmider
This paper is concerned with the isomorphic structure of the Banach space and how it depends on combinatorial tools whose existence is consistent but not provable…
On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts
Christina Brech, Piotr Koszmider
For k being the first uncountable cardinal w_1 or k being the cardinality of the continuum c, we prove that it is consistent that there is no Banach space of density k in which it…