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We define the crossed product of a pro-C*-algebra A by a Hilbert A-A pro-C*-bimodule and we show that it can be realized as an inverse limit of crossed products of C*-algebras by Hilbert C*-bimodules. We also prove that under some conditions the crossed products of two Hilbert pro-C*-bimodules over strongly Morita equivalent pro-C*-algebras are strongly Morita equivalent.
We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
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