Related papers: Closed and sigma-finite measures on the orthogonal…
We investigate the set-theoretic properties of the lattice of projections in the Calkin algebra of a separable infinite-dimensional Hilbert space in relation to those of the Boolean algebra $P(\omega)/{\rm fin}$, which is isomorphic to the…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content $\mu$. With…
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
A slight modification to Halmos' definition of product of measures yields a uniquely characterized associative product. The operation applies to arbitrary (not necessarily $\sigma-$finite) measures and is consistent with the Fubini--Tonelli…
The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…
We study the relationship between different kinds of convergence of finite signed measures and discuss their metrizability. In particular, we study the concept of basic convergence recently introduced by Khartov [arXiv:2204.13667] and…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line…
Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…
We derive upper bounds on the difference between the orthogonal projections of a smooth function $u$ onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the…
In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz…
The main goal of this work is to introduce an analogous in the non-archimedean context of the Gelfand spaces of certain Banach commutative algebras with unit. In order to do that, we study the spectrum of this algebras and we show that,…
We give a fresh account of the astonishing interplay between abelian von Neumann algebras, L^\infty-spaces and measure algebras, including an exposition of Maharam's theorem from the von Neumann algebra perspective.
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.