Semifinite traces on JBW-algebras

Abstract

A JB-algebra is a real Jordan algebra A which is also a Banach space and whose norm and multiplication satisfy the two following conditions(i) ∥a2∥ = ∥a∥2,(ii) ∥a2 − b2∥ ≤ max{∥a2∥, ∥b2∥},for all elements a and b in A. A JB-algebra which is also a Banach dual space is called a JBW-algebra. The properties of JB-algebras and JBW-algebras can be found in (3), (4), (8) and (15).