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Ignoring topological structures of von Neumann algebras, the larger category of Baer $*$-rings was emerged. In the unique text written by Sterling K. Berberian (1), some concepts and results in von ...

Let $A$ be a Baer $*$-ring. Let us denote $B$ by the space of all upper triangular matrices $\left(\begin{array}{cc} a_1& a_2 \\ 0 & a_4 \end{array}\right)$ where $a_i$'s are in $A$. Is $B$ ...

Let $A$ be a Baer*-ring with the unit $1$. An important point that holds in every Baer*-ring is this: for every element $y\in A$ there is an smallest projection $e_y\in A$, called the left projection ...

Assume $A$ is a complex $*$-algebra which is also a Baer*-ring. Q. Can we concluded that there exists a Hilbert space $H$ such that $A$ is embedded in $B(H)$ as a Baer*-ring? What about when $A$ ...

A Baer *-ring is an *-algebra whose lattice of projections is complete. I know two well-handed kinds of these structures: 1- W*-algebras (abstract case of von Neumann algebras). 2- The inverse ...

Let $A$ be a unital Baer *-ring. 1- Assume that $\{p_i\}$ is a family of projections in $A$. Let $x$ be an isometry in A (I mean $x^*x=1$ where $1$ is the unit of $A$). True or false: $\inf (...