Norms of Inner Derivations of Limit Algebras

Let A be a strongly maximal TAF-algebra. It is shown that $\frac{1}{2} \text{Orc} (A) \leq K (A) \leq \frac{4}{\sqrt{3}} \text{Orc}(A)$, where K(A) and Orc(A) are constants determined by the norms of inner derivations of A, and by the hull-kernel topology on the space of meet-irreducible ideals of A, respectively. It follows that the set of inner derivations of A is closed in the Banach space of all bounded derivations of A if and only if Orc(A) < ∞. These results are analogous to those for C*-algebras.