Related papers: A boundary projection for the dilation order

The existence of a well-behaved dimension of a finite von Neumann algebra (see [19]) has lead to the study of such a dimension of finite Baer *-rings (see [26]) that satisfy certain *-ring axioms (used in [9]). This dimension is closely…

We prove that any map between projection lattices of $AW^\ast$-algebras $A$ and $B$, where $A$ has no Type $I_2$ direct summand, that preserves orthocomplementation and suprema of arbitrary elements, is a restriction of a normal Jordan…

The paper studies projective freeness and Hermiteness of algebras of complex-valued continuous functions on topological spaces, Stein algebras, and commutative unital Banach algebras. New sufficient cohomology conditions on the maximal…

Every CSP(B) for a finite structure B is either in P or it is NP-complete but the proofs of the finite-domain CSP dichotomy by Andrei Bulatov and Dimitryi Zhuk not only show the computational complexity separation but also confirm the…

A birationally liftable Galois section s of a hyperbolic curve X/k over a number field k yields an adelic point x(s) in the smooth completion of X. We show that x(s) is X-integral outside a set of places of Dirichlet density 0, or s is…

In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the intersection of the subspaces is empty. His proof, which works…

We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we…

Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a…

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails. A motivational example of a problem…

Bi-Intuitionistic Stable Tense Logics (BIST Logics) are tense logics with a Kripke semantics where worlds in a frame are equipped with a pre-order as well as with an accessibility relation which is 'stable' with respect to this pre-order.…

We generalize fundamental notions of higher algebra, traditionally developed within the $\infty$-category of spectra, to the broader setting of $t$-structured tensor triangulated $\infty$-categories ($ttt$-$\infty$-categories). Under a…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

We first show that the union of a projective curve with one of its extremal secant lines satisfies the linear general position principle for hyperplane sections. We use this to give an improved approximation of the Betti numbers of curves…

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the…

In this paper, we introduce a notion of stable coarse algebras for metric spaces with bounded geometry, and formulate the twisted coarse Baum--Connes conjecture with respect to stable coarse algebras. We prove permanence properties of this…

It's well known that the functional Hilbert space over the unit ball in $B_{d} \in C^d$, with kernel function $K(z,w)=\frac{1}{1-z_{1}w_{1}-... -z_{d}w_{d}}$, admits a natural $A(B_{d})$-module structure. We show the rank of a nonzero…

In this paper, we introduce a partial order on rings with involution, which is a generalization of the partial order on the set of projections in a Rickart *-ring. We prove that a *-ring with the natural partial order form a sectionally…

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…

We study gapped boundaries of Abelian type-I fracton systems in three spatial dimensions. Using the X-cube model as our motivating example, we give a conjecture, with partial proof, of the conditions for a boundary to be gapped. In order to…