Cofinal Central Systems and Derivations

Abstract

Take an involutive algebra M₀ of bounded operators acting in the Hilbert space H, M₀ containing operators Ā ^-1_n for n ∈ N (with A₀ = Id, A_nD = D and D = ∩_n≥0 Ā ^-1_n (H) by hypothesis), such that the center of M₀ contains all Ā ^-1_n . Then it is clear that M₀ ⊂ L (D), and it follows that A = U_n≥0 M₀A_n × A_n is a ⋆-algebra, with natural domain D satisfying condition I, with all A_i as a cofinal central system.