Related papers: An absorption theorem for minimal AF equivalence r…

We prove a version of the Ando-Choi-Effros lifting theorem respecting subspaces, which in turn relies on Oja's principle of local reflexivity respecting subspaces. To achieve this, we first develop a theory of pairs of $M$-ideals. As a…

We find a precise relationship between the minimal extensions in $L^2$ and $L^p$ Ohsawa-Takegoshi extension theorems. This relationship also gives another proof to the $L^p$ version of the Ohsawa-Takegoshi extension theorem, which is…

In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…

The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining…

We establish a one-to-one correspondence between the set of minimal exponential families of dimension n defined on a finite sample space {\Omega} and the affine Grassmannian associated to an appropriate vector space of functions.

We construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f:R-->R with Cantor intermediate value property which is not almost continuous. This gives a…

The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to…

We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Caffarelli's contraction theorem to nearly spherical manifolds…

In 1994, J.Cobb constructed a tame Cantor set in $\mathbb R^3$ each of whose projections into $2$-planes is one-dimensional. We show that an Antoine's necklace can serve as an example of a Cantor set all of whose projections are…

In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.

We will show that an equivalence relation on a Cantor set arising from a two-dimensional substitution tiling by polygons is affable in the sense of Giordano, Putnam and Skau.

We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…

We lift the affine Matsuki correspondence between real and symmetric loop group orbits in affine Grassmannians to an equivalence of derived categories of sheaves. In analogy with the finite-dimensional setting, our arguments depend upon the…

Given two rings $R \subseteq S$, $S$ is said to be a minimal ring extension of $R$ if $R$ is a maximal subring of $S$. In this article, we study minimal extensions of an arbitrary ring $R$, with particular focus on those possessing nonzero…

For operators on Hilbert spaces of any dimension, we show that equivalence after extension coincides with equivalence after one-sided extension, thus obtaining a proof of their coincidence with Schur coupling. We also provide a concrete…

In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call…

For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge's theorem states lower semi-continuity of the minimum of this…

Any map of schemes $X\to Y$ defines an equivalence relation $R=X\times_Y X\to X\times X$, the relation of "being in the same fiber". We have shown elsewhere that not every equivalence relation has this form, even if it is assumed to be…

We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex…

An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…