Related papers: Lineability of non-differentiable Pettis primitive…
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the…
In 1992, Kiendi, Adamy and Stelzner investigated under which conditions a certain type of function constituted a Lyapunov function for some time-invariant linear system. Six years later, it was obtained that this property holds if and only…
The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of (intrinsic) Riemannian geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds. However, this…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
Two new applications of a technique for spaceability are given in this paper. For the first time this technique is used in the investigation of the algebraic genericity property of the weak form of Peano's theorem on the existence of…
We show that if $X$ is a complete metric space with uniform relative normal structure and $G$ is a subgroup of the isometry group of $X$ with bounded orbits, then there is a point in $X$ fixed by every isometry in $G$. As a corollary, we…
In this paper we study derivations in subalgebras of $L_{0}^{wo}(\nu ;% \mathcal{L}(X)) $, the algebra of all weak operator measurable funtions $f:S\to \mathcal{L}(X) $, where $% \mathcal{L}(X) $ is the Banach algebra of all bounded linear…
Read produced the first example of a Banach space $E_{\text{R}}$ such that the associated Banach algebra $\mathscr{B}(E_{\text{R}})$ of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalise Read's…
Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X)…
It was shown by Nachbin in 1950 that an $n$-dimensional normed space $X$ is injective or equivalently is an absolute 1-Lipschitz retract if and only if $X$ is linearly isometric to $l_\infty^n$ (i.e., $\mathbb{R}^n$ endowed with the…
In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed…
The primitive equations in a 3D infinite layer domain are considered with linearly growing initial data in the horizontal direction, which illustrates the global atmospheric rotating or straining flows. On the boundaries, Dirichlet, Neumann…
In this note we generalize a criterion within the concept of infinite dense lineability due to Calder\'on-Moreno, Gerlach-Mena and Prado-Bassas. We also introduce and explore some local notions of lineability.
We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford-Pettis criterion) coincides with the class of 1-disjointly homogeneous Banach…
We express the weight enumerator of each binary linear code, in particular the Ising partition function of an arbitrary finite graph, as a formal infinite product. An analogous result was obtained by Feynman and Sherman in the beginning of…
Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…
The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…
Our goal of this note is to give an easy proof that spaces of predictable processes with values in a Banach space are isomorphic to spaces of progressive resp. adapted, measurable processes. This provides a straightforward extension of the…
Inspired by the work of Hedenmalm, Lindqvist and Seip, we consider different properties of dilations systems of a fixed function $\varphi \in L^2(0,1)$. More precisely, we study when the system $\{\varphi(nx)\}_n$ is a Bessel sequence, a…