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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball  $$B_\mathfrak{A} $$  in a J*-algebra  $$\mathfrak{A}$$  of operators. Let  $$\mathfrak{F}$$  be the family of all collectively compact subsets W contained in  $$B_\mathfrak{A} $$ . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family  $$\mathfrak{F}$$  is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when  $$\mathfrak{A}$$  is a Cartan factor.

Holomorphic automorphisms and collective compactness in J*-algebras of operator