Derivations Tangential to Compact Group Actions: Spectral Conditions in the Weak Closure

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Abstract
Let G be a compact Lie group and a an action of G on a C*-algebra as *-automorphisms. Let denote the set of G-finite elements for this action, i.e., the set of those such that the orbit {αg(x):g ∊ G} spans a finite dimensional space. is a common core for all the *-derivations generating one-parameter subgroups of the action α. Now let δ be a *-derivation with domain such that Let us pose the following two problems: Is δ closable, and is the closure of δ the generator of a strongly continuous one-parameter group of *-automorphisms? If is simple or prime, under what conditions does δ have a decomposition where is the generator of a one-parameter subgroup of α(G) and is a bounded, or approximately bounded derivation?

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