Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping Φ:A→B satisfies Φ(a∘b+ba∗)=Φ(a)∘Φ(b)+Φ(b)Φ(a)∗ (where ∘ is the special Jordan product on B, respectively), for all elements a,b∈A, if only Φ ∗-ring isomorphism. particular, algebras are type I factors, then unitary isomorphism or conjugate

Injectivity with respect to morphisms having λ-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, λ-directed colimits, and λ-pure subobjects. This sharpens the result of the first two authors (Trans. Amer. Math. Soc. 336 (1993), 785-804). In contrast, for geometric logic an example is found of a class closed under directed col...

Figalli–Kim–McCann proved in [14] the continuity and injectivity of optimal maps under the assumption (B3) of nonnegative cross-curvature. In the recent [15, 16], they extend their results to the assumption (A3w) of Trudinger-Wang [34], and they prove, moreover, the Hölder continuity of these maps. We give here an alternative and independent proof of the extension to (A3w) of the continuity and...

This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distri...

Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional feature called counter. This paper proposes the notion of a Parikh rewriting system as a generalization and systematization of Salomaa’s result. It will be show...

One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebr...

Multivariate quasi-projection operators Qj(f,φ,φ˜), associated with a function φ and distribution/function φ˜, are considered. The is supposed to satisfy the Strang-Fix conditions compatibility condition φ˜. Using technique based on Fourier multipliers, we study approximation properties of such for functions f from anisotropic Besov spaces Lp 1≤p≤∞. In particular, upper lower estimates Lp-error...