Abstract
The present investigation was stimulated by a theorem of Alfsen and Effros (4.9 of [1]) concerning a real Banach space, its ikf-ideals, and its primitive M-ideals (these are denned in [1]). This theorem states that a real Banach space is in the natural way a module over the ring of bounded continuous real-valued functions on the space of primitive Jlf-ideals with the Jacobson topology.

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