相关论文: Singular MASAs in type III factors and Connes' Bic…

We prove that the Hardy--Littlewood maximal operator $M$ is bounded on the variable Lebesgue space $L^{p(\cdot)}(X,d,\mu)$, with $1<p_-\le p_+<\infty$, over an unbounded space of homogeneous type $(X,d,\mu)$ with a Borel-semiregular measure…

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda…

For systems with a finite number of degrees of freedom, it is shown in [arXiv:hep-th/0303014] that first class constraints are Abelianizable if the Faddeev-Popov determinant is not vanishing for some choice of subsidiary constraints. Here,…

In this paper, we will give a thorough study of the notion of Property $(T)$ for $C^*$-algebras (as introduced by M.B. Bekka in \cite{Bek-T}) as well as a slight stronger version of it, called "strong property $(T)$" (which is also an…

For a completely regular space $X$, let $C_B(X)$ be the normed algebra of all bounded continuous scalar-valued mappings on $X$ equipped with pointwise addition and multiplication and the supremum norm and let $C_0(X)$ be its subalgebra…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into…

We show that any compact group can be realized as the outer automorphism group of a factor of type II_1. This has been proved in the abelian case by Ioana, Peterson and Popa applying Popa's deformation/rigidity techniques to amalgamated…

We consider two von Neumann subalgebras $\cl B_0$ and $\cl B$ of a type ${\rm{II}}_1$ factor $\cl N$. For a map $\phi$ on $\cl N$, we define \[\|\phi \|_{\infty,2}=\sup\{\|\phi(x)\|_2\colon \|x\| \leq 1\},\] and we measure the distance…

We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the…

We show that, for every minimal action of a countably infinite discrete group on a compact metrizable space, if the extreme boundary of the simplex of invariant Borel probability measures is closed and has finite covering dimension then the…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…

We prove that whenever A is a 3-conservative relational structure with only binary and unary relations then the algebra of polymorphisms of A either has no Taylor operation (i.e. CSP(A) is NP-complete), or generates a congruence meet…

We construct a weakly compact convex subset of $\ell^2$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $\ell _+^2$. Moreover, the maximal point cannot be supported by any strictly positive…

Let $X$ be a compact metrizable space, and let $\Delta$ be a closed set of Borel probability measures on $X$. We study the small boundary property of the pair $(X, \Delta)$. In particular, it is shown that $(X, \Delta)$ has the small…

The Corona Factorization Property, originally invented to study extensions of C*-algebras, conveys essential information about the intrinsic structure of the C*-algebras. We show that the Corona Factorization Property of a \sigma-unital…

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying…

We prove that if a smoothly bounded strongly pseudoconvex domain $D \subset \mathbb C^n$, $n \geq 2$, admits at least one Monge-Amp\`ere exhaustion smooth up to the boundary (i.e. a plurisubharmonic exhaustion $\tau: \overline D \to [0,1]$,…

For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact…