Irreducible Jordan algebras of self-adjoint operators

1. Introduction. In In the present paper we shall complete the characterization of irreducible /IF-algebras by showing that they are all of type I. As a consequence we can generalize Kadison's result The key topological result for these investigations is Theorem 2.1, which gives estimates on the norms on operators in certain real algebras. As another application of this theorem we shall in 3 study the relationship between Jordan ideals in a reversible JC-or JW-algebra and two-sided ideals in the enveloping C*-or von Neumann algebra.

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