On the operator equation α+α−1=β+β−1 - A. B. Thaheem (International Journal of Mathematics and Mathematical Sciences)
Let α,β be ∗-automorphisms of a von Neumann algebra M satisfying the operator equation α+α−1=β+β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:- If α,β commute then there is a central projection p in M such that α=β on MP and α=β−1 on M(1−P); If M=B(H), the algebra of all bounded operators on a Hilbert space H, then α=β or α=β−1.