Related papers: Quojections without Banach subspaces

We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show…

We introduce the notion of subprojective and superprojective operators and we use them to prove a variation of the three-space property for subprojective and superprojective spaces. As an application, we show that some spaces considered by…

It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…

Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out…

For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a…

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c, the Banach space of null sequences under…

We construct a nonseparable Banach space $\mathcal X$ (actually, of density continuum) such that any uncountable subset $\mathcal Y$ of the unit sphere of $\mathcal X$ contains uncountably many points distant by less than $1$ (in fact, by…

We answer a question of Juhasz by constructing under CH an example of a locally connected continuum without nontrivial convergent sequences.

This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if $X$ is an arbitrary infinite-dimensional Banach space, $\{Y_n\}$ is a sequence of strictly nested subspaces of $ X$ and if $\{d_n\}$ is…

We generalize the notion of flat chains with arbitrary coefficient groups to Banach spaces and prove a sequential compactness result. We also remove the restriction that a flat chain have finite mass in order for its support to exist.

Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barrelled subspace of (algebraic) dimension $<\mbox{cov}(\mathcal{N})$, the covering number of the…

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular…

We investigate the quotients of Banach manifolds with respect to free actions of pseudogroups of local diffeomorphisms. These quotient spaces are called H-manifolds since the corresponding simply transitive action of the pseudogroup on its…

This paper considers explicit constructions of Auerbach bases in separable Banach spaces. Answering the question of A. Pe{\l}czy{\'n}ski, we prove by construction the existence of Auerbach basis in arbitrary subspace of $c_0$ of finite…

In this note, we extend to the setting of quasi-reflexive spaces a classical result of N. Kalton and L. Randrianarivony on the coarse Lipschitz structure of reflexive and asymptotically uniformly smooth Banach spaces. As an application, we…

Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces $A$ of maps from an arbitraty set to a sequence space, that, for every $0 \neq f \in A$, the subset of $A$ of…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping…

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms and establish some of their fundamental properties. We give much more detailed results about their structure…

Let $\{\tau_j\}_{j=1}^n$ be a collection in a finite dimensional Banach space $\mathcal{X}$ of dimension $d$ and $\{f_j\}_{j=1}^n$ be a collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) such that $f_j(\tau_j) =1$, $\forall 1\leq j\leq…