All Questions

A well-known generalization of the commutator for operators is the so-called q-commutator defined as $$[A,B]_q=AB-qBA.$$ I was wondering if the case where $q$ is not a number but other operator has ...

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bounded derivation. Can one say that $1$ can not be in the image of $D$? If the answer is no: What is a counter example? What kind of $...

A correspondence $_{N} H_{N}$ is a Hilbert space with two normal commuting left/right representations of $N$ in $B(H)$. The following characterization of property (T) for finite von Neumann algebras ...