Related papers: Linear maps between C*-algebras whose adjoints pre…

Let $\mathcal{A}$ and $\mathcal{B}$\ are $C^{{\huge \ast}}% $-algebras\textbf{.} A\textbf{ }linear map $\phi:\mathcal{A\rightarrow B}$ is $C^{\ast}$-Jordan homomorphism if it is a Jordan homomorphism which preserves the adjoint operation.…

We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible…

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…

We study surjective maps between the sets of all self-adjoint elements of unital $C^*$-algebras which satisfy the multiplicatively spectrum-preserving property. We show that such maps are characterized by Jordan isomorphisms and central…

We study maps between positive definite or positive semidefinite cones of unital $C^*$-algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplication of elements; (2) the spectrum of the quotient or…

We show that a bounded, linear map between C*-algebras is a weighted $\ast$-homomorphism (the central compression of a $\ast$-homomorphism) if and only if it preserves zero-products, range-orthogonality, and domain-orthogonality. It follows…

We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms.…

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products {a,b,c}= (ab*c + cb*a)/2. These include especially isometries and disjointness preserving operators.

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…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

Let T be be a zero-product preserving bounded linear map between C*-algebras A and B. Here neither A nor B is necessarily unital. In this note, we investigate when T gives rise to a Jordan homomorphism. In particular, we show that A and B…

We classify bijective maps which strongly preserve Birkhoff-James orthogonality on a finite-dimensional complex $C^*$-algebra. It is shown that those maps are close to being real-linear isometries whose structure is also determined.

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

We characterize when there exists a diagonal preserving $*$-isomorphism between two graph $C^*$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of "orbit equivalence" between the boundary…

We survey the results on linear local and 2-local homomorphisms and zero products preserving operators between C$^*$-algebras, and we incorporate some new precise observations and results to prove that every bounded linear 2-local…

Let $A,B$ be C*-algebras, $B_A(0;r)$ the open ball in $A$ centered at $0$ with radius $r>0$, and $H:B_A(0;r)\to B$ an orthogonally additive holomorphic map. If $H$ is zero product preserving on positive elements in $B_A(0;r)$, we show, in…

Recently, the question of whether surjective maps preserving the norm of a symmetric Kubo-Ando mean can be extended to Jordan $\ast$-isomorphisms has been tackled. The question was affirmatively answered for surjective maps between…

In this paper, we characterize a class of additive maps on Hilbert $C^\ast$-modules which maps a "rank one" adjointable operators to another rank one operators.