Related papers: Constructions of sequential spaces

We construct for each $0<p\le 1$ an infinite collection of subspaces of $\ell_p$ that extend the example from [J. Lindenstrauss, On a certain subspace of $\ell_{1}$, Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys. 12 (1964),…

In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is…

We study Banach spaces X with a strongly asymptotic l_p basis (any disjointly supported finite set of vectors far enough out with respect to the basis behaves like l_p) which are minimal (X embeds into every infinite dimensional subspace).…

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…

Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…

For a large class of Banach spaces, a general construction of subspaces without local unconditional structure is presented. As an application it is shown that every Banach space of finite cotype contains either $l_2$ or a subspace without…

It is shown that every Banach space either contains $\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\lambda )$, $1<p<\infty $, is a quotient of a H.I Banach space.

We study the dual space of the variable Lebesgue space $\Lp$ with unbounded exponent function $\pp$ and provide an answer to a question posed in~[fiorenza-cruzuribe2013]. Our approach is to decompose the dual into a topological direct sum…

A generalization of Lozanovskii's result is proved. Let E be $k$-dimensional subspace of an $n$-dimensional Banach space with unconditional basis. Then there exist $x_1,..,x_k \subset E$ such that $B_E \p \subset \p absconv\{x_1,..,x_k\}$…

Let $(e_i)_i$ denote the unit vector basis of $\ell_p$, $1\leq p< \infty$, or $c_0$. We construct a reflexive Banach space with an unconditional basis that admits $(e_i)_i$ as a uniformly unique spreading model while it has no subspace with…

For a separable rearrangement invariant space $X$ on $[0,1]$ of fundamental type we identify the set of all $p\in [1,\infty]$ such that $\ell^p$ is finitely represented in $X$ in such a way that the unit basis vectors of $\ell^p$ ($c_0$ if…

Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of…

Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…

Several new characterizations of Banach spaces containing a subspace isomorphic to $\ell^1$, are obtained. These are applied to the question of when $\ell^1$ embeds in the injective tensor product of two Banach spaces.

We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For $n\ge 2$ and $1<p<\infty$, it is shown that $\ell_\infty^n$ is representable in a Banach space $X$ if and only if it…

We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq…

In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…

We study ergodicity of composition operators on rearrangement-invariant Banach function spaces. More precisely, we give a natural and easy-to-check condition on the symbol of the operator which entails mean ergodicity on a very large class…

We give examples of two Banach spaces. One Banach space has no spreading model which contains $\ell_p$ ($1\le p<\infty$) or $c_0$. The other space has an unconditional basis for which $\ell_p$ ($1\le p<\infty$) and $c_0$ are block finitely…

We investigate certain recently introduced ODE-determined varying exponent $L^p$ spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent $\ell^p$ space. Moreover, this can be accomplished…