let $mathcal{a}$ and $mathcal{b}$ be two $c^{*}$-algebras such that $mathcal{b}$ is prime. in this paper, we investigate the additivity of maps $phi$ from $mathcal{a}$ onto $mathcal{b}$ that are bijective, unital and satisfy $phi(ap+eta pa^{*})=phi(a)phi(p)+eta phi(p)phi(a)^{*},$ for all $ainmathcal{a}$ and $pin{p_{1},i_{mathcal{a}}-p_{1}}$ where $p_{1}$ is a nontrivial projection in $mathcal{a...

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.

A positive map between Euclidean Jordan algebras is a (symmetric cone) order preserving linear map. We show that the norm of such a map is attained at the unit element, thus obtaining an analog of the operator/matrix theoretic Russo-Dye theorem. A doubly stochastic map between Euclidean Jordan algebras is a positive, unital, and trace preserving map. We relate such maps to Jordan algebra automo...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB + BA ∈ I(X ) implies φ(A)φ(B) + φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear s...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB +BA ∈ I(X ) implies φ(A)φ(B)+φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear surj...

In this paper, we give a complete description of the structure of zero product and orthogonality preserving linear maps between W*-algebras. In particular, two W*-algebras are *-isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions. It is also the case when they have equivalent linear and left (right) id...