Abstract

We show that if (X.A) and (Y,B) are two isomorphic Hilbert pro- C�-bimodules, then the crossed product A Z of A by X and the crossed product B ×Y Z of B by Y are isomorphic as pro-C � -algebras. We also prove a property of associativity between min and ×X as well as max and ×X. As an application of these results we show that the crossed product of a nuclear pro-C � -algebra A by a full Hilbert pro-C � -bimodule X is a nuclear pro-C � -algebra.

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