Related papers: Additivity and lineability in vector spaces

For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…

We further develop the relationship between $\beta$-numbers and discrete curvatures to provide a new proof that under weak density assumptions, finiteness of the pointwise discrete curvature $\operatorname{curv}^{\alpha}_{\mu;2}(x,r)$ at…

Let $k$ be a field, $V$ be a $k$-vector space and $X\subset V$ an algebraic irreducible subvariety. We say that a function $f:X(k) \to k$ is weakly linear if its restriction to any two-dimensional linear subspace $W$ of $V$ contained in $X$…

Let f be a non-negative concave function on the positive half-line. Let A and B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and…

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to a bounded linear operator $\widehat{f} : \mathcal F(M) \to \mathcal F(N)$ between their corresponding Lipschitz-free spaces. In this paper,…

We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an…

The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…

The famous Erdos-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdos-Heilbronn conjecture): For any…

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…

In this paper, with a view to improve the g-monotonicity condition, we introduce the notion of g-comparability of a mapping defined on an ordered set and utilize the same to prove some existence and uniqueness results on coincidence points…

Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the dimension of this subspace and on dim B^n in terms of dim A,…

We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…

We study countable saturation of the metric reduced products and introduce continuous fields of metric models indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the…

We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to…

For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} v$ in $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ in…

In this paper, we prove that the world of near-vector spaces allows us to work with non-linear problems and yet, gives access to most of the tools linear algebra has to offer. We establish some fundamental results for near-vector spaces…

The number theoretic analogue of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g > 1, the study of h-nets in the additive group of integers with…

Given a group $G$ and a family of subgroups $\mathcal{F}$, we consider its classifying space $E_{\mathcal F}G$ with respect to $\mathcal{F}$. When $\mathcal F = \mathcal{VC}yc$ is the family of virtually cyclic subgroups, Juan-Pineda and…

In this addendum we clarify a point which strengthens one of the results from [the original paper]. Namely, we show that the algebra of the observables $F(r,\theta)$ is yet simpler then it was described in [the original paper]. This is an…

We study when an additive mapping preserving orthogonality between two complex inner product spaces is automatically complex-linear or conjugate-linear. Concretely, let $H$ and $K$ be complex inner product spaces with dim$(H)\geq 2$, and…