In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

In this paper, we will use the categorical approach to Hilbert \(C^{\ast}\)-modules over a commutative \(C^{\ast}\)-algebra investigate approximately orthogonality preserving mappings on \(C^{\ast}\)-algebra. Indeed, show that if \(\Psi:\Gamma \rightarrow \Gamma^{\prime} \) is nonzero \( C_{0}(Z) \)-linear \(( \delta , \varepsilon)\)-orthogonality mapping between continuous fields of spaces loc...

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...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

In this paper, we present results concerning orthogonality in Hilbert C∗-modules. Moreover, for a C∗-algebra A, prove theorems the multi-A-linearity and its preservation byA-linear operators. New version of solution equation on C∗-modules mappings preserving are also investigated.