Lie and Jordan structure in operator algebras

Abstract

Let 91 be a C*-algebra, α a *-anti-automorphism of order 2, and (+ 1) = {A; AεU, α(A) = ±A} the spectral subspaces of α. It follows that uα(+l) is a Jordan algebra and uα(—1) is a Lie algebra. We begin the classification of pairs of Jordan and Lie algebras which can occur in this manner by examining U-L(H), the algebra of bounded operators on a Hilbert space X. Show more