Crossed products by Hilbert pro-$C^{\ast }$-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.
