2017/12/17 by Kosenko, Petr
#46H05 #46H25 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1712.06178
For an Arens-Michael algebra A we consider a class of A-⊗-bimodules which are invertible with respect to the projective bimodule tensor product. We call such bimodules topologically invertible over A. Given a Fréchet-Arens-Michael algebra A and an topologically invertible Fréchet A-⊗-bimodule M, we construct an Arens-Michael algebra \widehatLA(M) which serves as a topological version of the Laurent tensor algebra LA(M). Also, for a fixed algebra B we provide a condition on an invertible B-bimodule N sufficient for the Arens-Michael envelope of LB(N) to be isomorphic to \widehatL_\widehatB(\widehatN). In particular, we prove that the Arens-Michael envelope of an invertible Ore extension A[x, x-1; α] is isomorphic to \widehatL_\widehatA(\widehatA\widehatα) provided that the Arens-Michael envelope of A is metrizable.