Related papers: Zero product preservers of C*-algebras

We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)),…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a…

Let $\mathcal{A}$ and $\mathcal{B}$ be two factor von Neumann algebras and $\eta$ be a non-zero complex number. A nonlinear bijective map $\phi:\mathcal A\rightarrow\mathcal B$ has been demonstrated to satisfy…

We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…

We show that finite-dimensional order unit spaces equipped with a continuous sequential product as defined by Gudder and Greechie are homogeneous and self-dual. As a consequence of the Koecher-Vinberg theorem these spaces therefore…

We say that an algebra is zero-product balanced if $ab\otimes c$ and $a\otimes bc$ agree modulo tensors of elements with zero-product. This is closely related to but more general than the notion of a zero-product determined algebra of…

We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan $^*$-isomorphisms. In particular, we prove that two von Neumann algebras without…

Let $\eta\neq -1$ be a non-zero complex number, and let $\phi$ be a not necessarily linear bijection between two von Neumann algebras, one of which has no central abelian projections preserving the Jordan $\eta$-$\ast$-$n$-product. It is…

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial projections in $\mathfrak{A}$. In this paper we…

Given a Jordan algebra $A$ and a vector space $V$, we describe and classify all Jordan algebras containing $A$ as a subalgebra of codimension ${\rm dim}_k (V)$ in terms of a non-abelian cohomological type object ${\mathcal J}_{A} \, (V, \,…

Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear…

If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n / \bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic's Axiom and Martin's Axiom, that every isomorphism between two reduced products of separable,…

Let H and K be infinite dimensional Hilbert spaces, while B(H) and B(K) denote the algebras of all linear bounded operators on H and K, respectively. We characterize the forms of additive mappings from B(H) into B(K) that preserve the…

We investigate linear operators between C$^\ast$-algebras which approximately preserve involution and orthogonality, the latter meaning that for some $\varepsilon>0$ we have $\|\phi(x)\phi(y)\|\leq\varepsilon\|x\|\|y\|$ for all positive…

Applying a result of abstract ring theory we get that bijective additive mappings on standard algebras of unbounded operators preserving zero products are multiples of ring isomorphisms. The structure of additive bijective mappings on…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

We provide a complete description of the order isomorphisms between the self-adjoint parts of $C^*$-algebras. Furthermore, we characterize such isomorphisms between general operator intervals in $AW^*$-algebras. For the description, we use…