On bounded and unbounded idempotents whose sum is a multiple of the identity

Yurii Samoilenko, Lyudmila Turowska

We study bounded and unbounded representations of the $\ast$-algebra $Q_{n,\lambda }(\ast )$ generated by $n$ idempotents whose sum equals $\lambda e$ ($\lambda \in \mathbb{C}$, $e$ is the identity).