JB-algebras

Abstract

This chapter starts with the definition and basic properties of JBalgebras. We show that quotients of JB-algebras are again JB-algebras, and that Jordan isomorphisms between JB-algebras are isometries.Next we investigate properties of compressions(maps a→{pbp}forpa projection);these will play a key role in our axiomatic investigations in Part II. This is followed by a discussion of operator commutativity (the Jordan analog of the associative notion of commutativity).The chapter ends with basic facts about order derivations on JB-algebras.(In Chapter 6, we will discuss order derivations in more detail.)