arXiv subjects
Publications and source records attributed to Hamid Rohi.
Let $\mathcal{A}$ be a factor von Neumann algebra and $ϕ$ be the $\ast$-Jordan derivation on $A$, that is, for every $A,B \in \mathcal{A}$, $ϕ(A\diamond_{1} B) = ϕ(A)\diamond_{1} B + A\diamond_{1}ϕ( B)$ where $A\diamond_{1} B = AB + BA^{\ast}$, then $ϕ$ is additive $\ast$-derivation.
Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{B}$ is prime. In this paper, we investigate the additivity of map $Φ$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies $$Φ(AP+ηPA^{*})=Φ(A)Φ(P)+ηΦ(P)Φ(A)^{*},$$ for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial projection in $\mathcal{A}$. Let $η$ be a non-zero complex number such that $|η|\neq1$, then $Φ$ is additive. Moreover, if $η$ is rational then $Φ$ is $\ast$-additive.
Let $\mathcal{A}$ and $\mathcal{B}$ be two prime $C^{*}$-algebras. In this paper, we investigate the additivity of map $Φ$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies $$Φ(AP+λPA^{*})=Φ(A)Φ(P)+λΦ(P)Φ(A)^{*},$$ for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial projection in $\mathcal{A}$ and $λ\in\{-1,+1\}$. Then, $Φ$ is $*$-additive.
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.