Related papers: Basic sequences and spaceability in $\ell_p$ space…

We consider elliptic surfaces $\mathcal{E}$ over a field $k$ equipped with zero section $O$ and another section $P$ of infinite order. If $k$ has characteristic zero, we show there are only finitely many points where $O$ is tangent to a…

For any group $G$ containing an infinite elementary amenable subgroup, and any $2<p<\infty$, there exists closed invariant subspaces $E_i\nearrow \ell^pG$ and $F\neq 0$ such that $E_i\cap F = 0$ for all $i$. This is an obstacle to…

Let $\mathcal{M}$ be a semifinite von Neumann algebra. We equip the associated noncommutative $L_p$-spaces with their natural operator space structure introduced by Pisier via complex interpolation. On the other hand, for $1<p<\infty$ let…

Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset\dots$. We prove that this sequence admits Lipschitz retractions $X(n)\to X(n-1)$ when $X$ is a Hilbert space.

Let $1\le p <\infty$, $f\in L_p(\real)$ and $\Lambda\subseteq \real$. We consider the closed subspace of $L_p(\real)$, $X_p (f,\Lambda)$, generated by the set of translations $f_{(\lambda)}$ of $f$ by $\lambda \in\Lambda$. If $p=1$ and…

This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…

It is shown that the weak $L^p$ spaces $\ell^{p,\infty}, L^{p,\infty}[0,1]$, and $L^{p,\infty}[0,\infty)$ are isomorphic as Banach spaces.

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…

A Banach space X is said to have the Tsirelson property if it does not contain subspaces that are isomorphic to l_{p}, p in [1,infty) or c_{0}. The article contains a quite simple method to producing Banach spaces with the Tsirelson…

We investigate some general questions in algebraic dynamics in the case of generic endomorphisms of projective spaces over a field of characteristic zero. The main results that we prove are that a generic endomorphism has no non-trivial…

We prove that the subspace $c_0$ of sequences that converge to zero is not complemented in the space $ac_0$ of sequences that almost converge to zero. We proceed with applying the same approach to inclusion chain $c_0\subset A_0 \subset…

In this paper we first define the $\bar{N}(p,q)$ summable sequence spaces and obtain some basic results related to these spaces. The necessary and sufficient conditions for infinite matrices $A$ to map these spaces on $X~~,~~X=c_0, c \text{…

We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into…

We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of…

Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces…

Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if $X$ is a countably compact space and $C_p(X)$ is a space of continuous functions in the pointwise topology…

The endomorphism ring End(A) of an abelian variety A is an order in a semi-simple algebra over Q. The co-index of End(A) is the index to a maximal order containing it. We show that for abelian varieties of fixed dimension over any…

We consider the question whether there exists a Banach space $X$ of density continuum such that every Banach space of density not bigger than continuum isomorphically embeds into $X$ (called a universal Banach space of density $\cc$). It is…

We introduce a new approach that allows us to determine the structure of Zhu's algebra for certain vertex operator (super)algebras which admit horizontal $\mathbb{Z} $-grading. By using this method and an earlier description of Zhu's…

In our paper [18] we showed that a Tychonoff space $X$ is a $\Delta$-space (in the sense of [20], [30]) if and only if the locally convex space $C_{p}(X)$ is distinguished. Continuing this research, we investigate whether the class $\Delta$…