Abstract
In this paper, we prove a universal property for the crossed product of a pro-\(C^{*}\)-algebra by an inverse limit action of a locally compact group. Also, we prove a universal property of the crossed product of a Hilbert (pro-) \(C^{*}\)-module by an (inverse limit) action of a locally compact group.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arambašić, Lj.: Irreducible representations of Hilbert \(C^{\ast }\)-modules. Math. Proc. R. Ir. Acad. 105A(1), 11–24 (2005)
Fragoulopoulou, M.: Topological Algebras with Involution. North Holland, Amsterdam (2005)
Joiţa, M.: Crossed Products of Locally \(C^{\ast }\)-Algebras, pp. 115+Xii, Editura Academiei Române, Bucharest (2007). ISBN 978-973-27-1600-7
Joiţa, M.: Hilbert Modules Over Locally \(C^{\ast } \)-Algebras. University of Bucharest Press, Bucharest (2006)
Joiţa, M.: Crossed products of pro-\(C^{\ast }\)-algebras and strong Morita equivalence. Mediterr. J. Math. 5(4), 467–492 (2008)
Joiţa, M.: On Lebesgue type decomposition for covariant completely positive maps on \(C^{\ast }\)-algebras. Banach J. Math. Anal. 4(2), 75–85 (2010)
Joiţa, M.: Covariant representations of Hilbert \(C^{\ast }\)-modules. Expo. Math. 30, 209–220 (2012)
Kusuda, M.: Duality for crossed products of Hilbert \(C^{\ast }\)-modules. J. Oper. Theory 60(1), 85–112 (2008)
Mallios, A.: Topological Algebras: Selected Topics. North Holland, Amsterdam (1986)
Phillips, N.C.: Inverse limits of \(C^{\ast }\)-algebras. J. Oper. Theory 19, 159–195 (1988)
Phillips, N.C.: Representable K-theory for \(\sigma - C^{\ast }\)-algebras. K-Theory 3(5), 441–478 (1989)
Raeburn, I.: On crossed products and Takai duality. Proc. Edinb. Math. Soc. 31, 321–330 (1988)
Raeburn, I., Thompson, S.J.: Countably generated Hilbert modules, the Kasparov stabilisation theorem, and frames with Hilbert modules. Proc. Amer. Math. Soc. 131(5), 1557–1564 (2003)
Sharifi, K.: Generic properties of module maps and characterizing inverse limits of \(C^{\ast }\)-algebras of compact operators. Bull. Malays. Math. Sci. Soc. 36(2), 481–489 (2013)
Williams, D.P.: Crossed Products of \(C^{\ast }\)-Algebras, Mathematical Surveys and Monographs, vol. 134. American Mathematical Society, Providence (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Mohammad Sal Moslehian.
Rights and permissions
About this article
Cite this article
Joiţa, M. Crossed Products of Pro-\(C^{*}\)-Algebras and Hilbert Pro-\(C^{*}\)-Modules. Bull. Malays. Math. Sci. Soc. 38, 1053–1065 (2015). https://doi.org/10.1007/s40840-014-0067-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-014-0067-z