Related papers: Direct and inverse limits of normed modules
In the language of $L^\infty$-modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space $(M,\mathfrak{m})$ carrying a quasi-regular, strongly local Dirichlet form $\mathscr{E}$. Furthermore, we…
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and…
The category of level zero representations of current and affine Lie algebras shares many of the properties of other well-known categories which appear in Lie theory and in algebraic groups in characteristic p and in this paper we explore…
Given an upward directed set $I$ we consider surjective $I$-inverse systems $\{X_\al,f_{\al\be}:X_\be\lra X_\al| \al\leq\be\in I\}$, namely those inverse systems that have all $f_{\al\be}$ surjective. A number of properties of $I$-inverse…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
We prove matching direct and inverse theorems for uniform polynomial approximation with $A^*$ weights (a subclass of doubling weights suitable for approximation in the $L_\infty$ norm) having finitely many zeros and not too "rapidly…
The main objective of this article is to study several generalizations of the reverse order law for the Moore-Penrose inverse in ring with involution.
We consider positive Jacobi matrices $J$ with compact inverses and consequently with purely discrete spectra. A number of properties of the corresponding sequence of orthogonal polynomials is studied including the convergence of their…
Let G be a Lie group which is the union of an ascending sequence of Lie groups G_n (all of which may be infinite-dimensional). We study the question when G is the direct limit of the G_n's in the category of Lie groups, topological groups,…
The aim of this paper is to introduce and study graded and filtered gamma rings and gamma modules. We prove that the filtered $\Gamma$-ring (module) is a generalization of the notion of graded ring (module). Also, we construct a graded…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
In this paper, we study a class of $\Z_d$-graded modules, which are constructed using Larsson's functor from $\sl_d$-modules $V$, for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the…
We study the ends of a generic manifold, with respect to a unimodular measure on the space of pointed Riemannian manifolds with bounded curvatures. We apply our general result to the case of surfaces and obtain as corollaries a very precise…
This paper, in the setting at infinity, presents some relationships between the modulus of metric regularity and the radius of (strong) metric regularity that gives a measure of the extent to which a set-valued mapping can be perturbed…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
The dual modular propinquity is a complete metric, up to full modular quantum isometry, on the class metrical quantum vector bundles, i.e. of Hilbert modules endowed with a type of densely defined norm, called a D-norm, which generalize the…
This note briefly reviews the {\it Mirror Principle} as developed in the series of papers \LLYI\LLYII\LLYIII\LLYIV\LCHY. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting…
It is shown that nodal sequences determine the underlying manifold up to scaling within classes of rectangles with Dirichlet boundary conditions, separable two dimensional tori, two-dimensional flat Klein bottles and flat tori in two and…
We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from a Poincare' decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in…