# Questions tagged [baer-rings]

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### Algebraic language of fundamental results in operator algebras

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 ...
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### Relation between left projections

Let $A$ be a Baer *-ring. Let $x$ be in $A$, $L(x)$ is the left projection of $x$ that is the smallest projection with $L(x)x=x$. Q. Let $p,q$ are projections in $A$ with $p\leq q$. For a given ...
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### Algebraic version of unilateral shift

It was confirmed that Wold-type decomposition can be extended from von Neumann algebras to Baer*-rings (see this paper). By algebraic tools the notion of unilateral shifts is successfully transmitted ...
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### shifts in Baer*-rings

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 ...
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### When does a projection commute with an element?

Let $A$ be a Baer*-ring and $a$ be in $A$. Assume that for a projection $p\in A$, the following system of equations hold: \begin{array}{ll} a^na^{*n}p=p , & n\geq0\\ a^{*n}a^np=p , &...
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### Is $M_n(Z_p)$ a Baer*-ring?

Let $p$ be a prime number and $n$ be a natural number. Does $M_n({\mathbf{Z}}_p)$, the ring of all $n\times n$ matrices over the field ${\mathbf{Z}}_p$ form a Baer*-ring? If not, what about for ...
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### Does the inequality $x^2\leq x$ hold in Baer*-ring for $0 \leq x \leq 1$?

Let $A$ be a Baer*-ring and $x$ be a positive element with $0\leq x\leq1$ where $1$ is just the unit of $A$. Can we conclude $x^2\leq x$?
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### A Baer *-ring which is not embedded into $B(H)$

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 $A$ ...
Let $A$ be a unital Baer*-ring. We say that $a$ is a contraction if $aa^*\leq1$ and $a^*a\leq1$. Q1) Assume $a$ is a contraction. Has the positive element $1-aa^*$ any square root? (if yes, seems $1-... 3answers 182 views ### Some non-trivial Baer *-rings A Baer *-ring is an *-algebra whose lattice of projections is complete. I know two well-handed kinds of these structures: 1- W*-algebras (abstract case of von Neumann algebras). 2- The inverse ... 1answer 78 views ### Two points concerning Baer *-rings Let$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 (...
It is known that a reduced commutative unitary Baer ring $A$ is normal iff for every prime ideal $\mathfrak p$ of $T(A)$ (here $T(A)$ is the total quotient of $A$) one has $A/(\mathfrak p\cap A)$ is ...