In present talk we deal with the class $\mathcal{C}=\mathcal{C}_1\cup \mathcal{C}_2$ where $\mathcal{C}_1$ (respectively, $\mathcal{C}_2$) is formed by all separable Uniform algebras (respectively, separable commutative C$^*$-algebras) with no compact elements. For a given algebra $A$ in $\mathcal{C}_1$ (respectively, $A$ in $\mathcal{C}_2$) we show that $A$ is isometrically...
Let $\mathcal{M}$ be a $\ast$-algebra with unity $I$ and a non-trivial projection $P$. For any $D, E \in \mathcal{M}$, the operations $
D \diamond E = DE + ED \quad \text{and} \quad D \bullet E = DE + ED^\ast
$ are known respectively as the Jordan product and the Jordan $*$-product. If a map $\Omega: \mathcal{M} \to \mathcal{M}$ such that
\begin{eqnarray*}
\Omega(D_1 \diamond D_2...
This article aims to demonstrate the following: consider V, a CSL subalgebra of a von Neumann algebra acting on a Hilbert space H. Suppose that G, F : V → V are two linear mappings that satisfy some certain functional identities. Then G is a generalized (η, φ)-derivation with associated (η, φ)-derivation F in V, where η and φ are automorphisms in V.
