Related papers: Complete isometries between subspaces of noncommut…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first…

We give a numerical characterization of mutual orthogonality (that is, complementarity) for subalgebras. In order to give such a characterization for mutually orthogonal subalgebras $A$ and $B$ of the $k \times k$ matrix algebra…

In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…

The notion of the ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces. In this paper, we provide ultrametric versions of the…

Let $\mathcal{M}$ be a von Neumann algebra, and let $0<p,q\le\infty$. Then the space $\Hom_\mathcal{M}(L^p(\mathcal{M}),L^q(\mathcal{M}))$ of all right $\mathcal{M}$-module homomorphisms from $L^p(\mathcal{M})$ to $L^q(\mathcal{M})$ is a…

We study finite subsets of $\ell_p$ and show that, up to nowhere dense and Haar null complement, all of them embed isometrically into any Banach space that uniformly contains the spaces $\ell_p^n$, $n \in \mathbb{N}$.

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…

We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning separable spaces appeared in various papers in the last…

The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…

Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space…

Noncommutative domain algebras were introduced by Popescu as the non-selfadjoint operator algebras generated by weighted shifts on the Full Fock space. This paper uses results from several complex variables to classify many noncommutative…

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

Almost-isometries are quasi-isometries with multiplicative constant one. Lifting a pair of metrics on a compact space gives quasi-isometric metrics on the universal cover. Under some additional hypotheses on the metrics, we show that there…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

We studied complex interpolation noncommutative Hardy space associated with semi-finite von Neumann algebra and extend Pisier's interpolation theorem for this case.

We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral.…

We describe the T-space of central polynomials for both the unitary and the nonunitary infinite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pelczynski subsequence decomposition of bounded sequences in L^p[0,1] to the case of the Haagerup L^p-spaces (1\le p<\infty).…