Crossed products by Hilbert pro--bimodules
Volume 215 / 2013
Studia Mathematica 215 (2013), 139-156
MSC: Primary 46L05, 46L08; Secondary 46L55, 46H25.
DOI: 10.4064/sm215-2-4
Abstract
We define the crossed product of a pro-C^{*}-algebra A by a Hilbert A\text {-}\hskip -1pt 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^{\ast }-bimodules over strongly Morita equivalent pro-C^{\ast }-algebras are strongly Morita equivalent.