Related papers: Factorizations for quasi-Banach time-frequency spa…

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…

This paper investigates factorial $W^*$-bundles and their ultraproducts. More precisely, a $W^*$-bundle is factorial if the von Neumann algebras associated to its fibers are all factors. Let $M$ be the tracial ultraproduct of a family of…

We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form $(Z/nZ)\sqcup\{0\}$ (where 0 is a new zero element), for positive integers $n$. The key properties…

For $0 \leq \alpha < n$ and $m \in \mathbb{N} \cap \left(1 - \frac{\alpha}{n}, +\infty \right)$, we consider certain fractional type operators $T_{\alpha, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < \alpha < n$,…

We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$ and a maximally modulated Calder\'on-Zygmund singular integral operator…

We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…

$C^*$-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is…

Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…

We prove sharp estimates for the dilation operator $f(x)\longmapsto f(\lambda x)$, when acting on Wiener amalgam spaces $W(L^p,L^q)$. Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations…

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the…

We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular…

In this note we study simple modules for a reduced enveloping algebra U_chi(g) in the critical case when chi element of g^* is ``nilpotent''. Some dimension formulas computed by Jantzen suggest modified versions of Weyl's dimension formula,…

We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a…

We present simple conditions which guarantee a geometric convolution algebra to behave like a variant of the quasi-hereditary algebra. In particular, standard modules of the affine Hecke algebras of type $\mathsf{BC}$, and the quiver Schur…

Let $G$ be the Weil restriction of a general linear group. By extending the method of semi-modules developed by de Jong, Oort, Viehmann and Hamacher, we obtain a stratification of the affine Deligne-Lusztig varieties for $G$ (in the affine…

In this paper we first prove the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ spaces. Using Gabor frame representation this implies that the same property holds in weighted modulation and Wiener amalgam…

We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$,…

Let $G$ be an infinite locally compact abelian group. If $X$ is Banach space, we show that if every bounded Fourier multiplier $T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on $L^2(G,X)$ then the Banach space $X$ is…

Let $(X,\bullet )$ be a groupoid (binary algebra) and $Bin(X\dot{)}$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product \textquotedblleft…

Recently, J.X. Chen et al. introduced and studied the class of almost limited sets in Banach lattices. In this paper we establish some characterizations of almost limited sets in Banach lattices (resp. wDP* property of Banach lattices),…