INVOLUTIVE GRADINGS AND KERNELS IN JBW*-TRIPLES

Abstract

Involutive automorphism, or bijective triple homorphisms of order two, on a JBW *-triple are in a one-to-one correspondence with involutive gradings and bicontractive projections. Such mappings are always isometric and weak*-continuous. This paper analyses the algebraic kernels of the 1-eigenspace B+ and -1-eigenspace B- of involutive automorphisms. It is shown that B+ and B- give rise to several decompositions of A and, remarkably, Ker (B+) and Ker (B-) are Peirce inner ideals.