Related papers: Weak compactness and strongly summing multilinear …

The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…

In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

Let E be a Dedekind complete Riesz space with weak unit e, equipped with a conditional expectation operator T. We prove that the spaces Lp(T), with their natural vector-valued norms, are strongly complete, extending the p=2 case of Kuo,…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…

Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. The theory of operator spaces provides a set up which describes 4 norm optimal factorizations of Grothendieck's sort.…

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,…

Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous…

We give an example of an operator with different weak and strong absolutely continuous subspaces, and a counterexample to the duality problem for the spectral components. Both examples are optimal in the scale of compact operators.

We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…

Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective,…

We show that the strong operator topology, the weak operator topology and the compact-open topology agree on the space of unitary operators of a infinite dimensional separable Hilbert space. Moreover, we show that the unitary group endowed…

We show that the existence of a weakly compact cardinal over the Zermelo-Fraenkel's set theory is proof-theoretically reducible to iterations of Mostowski collapsings and Mahlo operations.

We study compactness and L\"owenheim-Skolem properties of fragments of the class-sized logic $\mathcal{L}_{\infty \infty}$ and of class-sized versions of second-order and sort logics. In these fragments, certain combinations of infinitary…

We present sharp interpolation theorems, including all limiting cases, for a class of quasilinear operators of joint weak type acting between Lorentz-Karamata spaces over $\sigma$-finite measure. This class contains many of the important…

We provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformations with respect to some nondegenerate Gaussian measure. These…

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…

It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…

The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces…