Related papers: Maximal noncompactness of embeddings into Marcinki…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on…
In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an…
The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schr\"odinger operator has a finite or infinite number of the discrete pectrum. In…
We give an alternative proof of a Marcinkiewicz interpolation theorem for non commutative maximal functions and positive maps, slightly refining earlier versions of the statement. The main novelty is that it provides a substitute for the…
A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the…
We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…
Quasianalytic contractions form the crucial class in the quest for proper invariant and hyperinvariant subspaces for asymptotically non-vanishing Hilbert space contractions. The property of quasianalycity relies on the concepts of unitary…
We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositions id = \sum x_j \otimes x_j, rather than on the coordinate one. The John's decomposition brings this result to the local…
We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremum spaces with Lyapunov type functions and local domination.…
A multiple operator integral (MOI) is an indispensable tool in several branches of noncommutative analysis. However, there are substantial technical issues with the existing literature on the "separation of variables" approach to defining…
We prove a generalisation of the disintegration theorem to the setting of multifunctions between Polish probability spaces. Whereas the classical disintegration theorem guarantees the disintegration of a probability measure along the…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
Let $(\mathbb{X},d,\mu)$ be a space of homogeneous type in the sense of R. R. Coifman and G. Weiss, and $X(\mathbb{X})$ a ball quasi-Banach function space on $\mathbb{X}$. In this article, the authors introduce the weak Hardy space…
This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…
This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema. We study general properties of such…
Let $Q$ denote the space of signed measures on the Borel $\sigma$-algebra of a separable complete space $X$. We endow $Q$ with the norm $\|q\|=\sup|\int\phi dq|$, where the supremum is taken over all Lipschitz with constant 1 functions…
In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach…
We characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure. Using the same tools in the proof of…