Related papers: Isometries of absolute order unit spaces

Let $\mathcal{J}$ be the exceptional Jordan algebra and $V=\mathcal{J}\oplus \mathcal{J}$. We construct an equivariant map from $V$ to $\mathrm{Hom}_k(\mathcal{J}\otimes \mathcal{J},\mathcal{J})$ defined by homogeneous polynomials of degree…

We show that if A is a linear order then Th(A) is either $\aleph_0$-categorical or Borel complete (in the sense of Friedman and Stanley). We generalize this; if A has countably many unary predicates attached, then Th(A) is…

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…

An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application…

The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…

We characterize the surjective isometries, with respect to the Hausdorff distance, of the class of bodies given by intersections of Euclidean unit balls. We show that any such isometry is given by the composition of a rigid motion with…

Under the mild condition of continuity at a single point we describe all the bijections of the set of all partial isometries on a Hilbert space which preserve the order and the orthogonality in both directions. Moreover, we present a…

Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are…

Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\otimes M_{n_i}(\mathbb{F})$ of matrix algebras over a field $\mathbb{F}$, and (2) the Clifford algebra of a nondegenerate…

An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric…

Let $\mathbb{H}^n$ be the $n-$dimensional hyperbolic space. It is well known that, if $f: \mathbb{H}^n\to \mathbb{H}^n$ is a bijection that preserves $r-$dimensional hyperplanes, then $f$ is an isometry. In this paper we make neither…

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

An algebraic isopair is a commuting pair of pure isometries that is annihilated by a polynomial defining a distinguished variety $\mathcal{V}$. The notion of the rank of a pure algebraic isopair with finite bimultiplicity is introduced. For…

We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly…

Let $\mathbb F$ be an algebraically closed field, $G$ be an abelian group, and let $A$ and $B$ be arbitrary finite-dimensional $G$-graded simple algebras over $\mathbb F$. We prove that $A$ and $B$ are isomorphic if, and only if, they…

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…

We show that a map between projection lattices of semi-finite von Neumann algebras can be extended to a Jordan $*$-homomorphism between the von Neumann algebras if this map is defined in terms of the support projections of images (under the…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

In this paper we prove that an isometry between orbit spaces of two proper isometric actions is smooth if it preserves the codimension of the orbits or if the orbit spaces have no boundary. In other words, we generalize Myers-Steenrod's…

We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a…