Related papers: On quantitative Schur and Dunford-Pettis propertie…

A Banach space $X$ has Pe{\l}czy\' nski's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ is weakly compact. In 1962, Aleksander Pe{\l}czy\' nski showed that $C(K)$ spaces for a compact…

In this paper, using a relationship between the Schur multiplier of a group $G$, the fundamental group, and the second homology group of the Eilenberg-MacLane space of $G$, we present new proofs for some famous properties of the Schur…

In spaces of metrics, we investigate topological distributions of the doubling property, the uniform disconnectedness, and the uniform perfectness, which are the quasi-symmetrically invariant properties appearing in the David--Semmes…

We show that the validity of the non-commutative Khintchine inequality for some $q$ with $1<q<2$ implies its validity (with another constant) for all $1\le p<q$. We prove this for the inequality involving the Rademacher functions, but also…

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on…

In this paper, we prove that for every compact set of the unit disk of logarithmic capacity 0, there exists a Schur function both in the disk algebra and in the Dirichlet space such that the associated composition operator is in all…

Inspired by the work of Z. Lu and G. Tian \cite{lutian}, in this paper we address the problem of studying those \K\ manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the $k$-th power of the…

A Banach space $X$ has \textit{property $(K)$}, whenever every weak* null sequence in the dual space admits a convex block subsequence $(f_{n})_{n=1}^\infty$ so that $\langle f_{n},x_{n}\rangle\to 0$ as $n\to \infty$ for every weakly null…

We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules…

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.

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikod\'ym property. We also show that the Lipschitz free space over a complete, locally compact metric space has the Schur or approximation…

We describe the action of the infinite-dimensional Lie algebra $W_{1+\infty}$ and its B-type analogue on Schur and Schur Q-functions, respectively, using formal distributions framework. We observe an interesting self-duality property…

We prove a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional,…

We study $N=1$ supersymmetric $SP(N_c)$ gauge theories with $N_f$ flavors of quarks in the fundamental representation. Depending on $N_f$ and $N_c$, we find exact, dynamically generated superpotentials, smooth quantum moduli spaces of…

We determine the complete spacetime action to first order in $\alpha'$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal…

The Peterson variety is a subvariety of the flag manifold $G/B$ equipped with an action of a one-dimensional torus, and a torus invariant paving by affine cells, called Peterson cells. We prove that the equivariant pull-backs of Schubert…

Let $M$ be a $3$-manifold, compact with boundary and $\Gamma$ its fundamental group. Consider a complex reductive algebraic group G. The character variety $X(\Gamma,G)$ is the GIT quotient $\mathrm{Hom}(\Gamma,G)//G$ of the space of…

Gelfand-Naimark duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to $C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces. Using this duality, we give for an \emph{arbitrary}…

Some key features of the symmetries of the Schr\"odinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving first and…