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So much is known about hermitian and non-hermitian idempotents in a $C^*$-algebra, that someone must have written down the following. Theorem The universal $C^*$-algebra generated by one element $x$...

Let $A$ be a Banach or a $C^*$ algebra. We consider the differential equation $$(*)\;\;\;\;Z'=Z^2-Z$$ on $A$. Obviously the singularities of this systems are just the idempotents of the ...

Let $H$ and $K$ be Hilbert spaces and $B(H,K)$ denotes the space of bounded operators from $H$ to $K$. Recall that a ternary ring of operators (TRO) $V$ is a closed subspace of $B(H,K)$ which is ...