Abstract
In this paper the tensor products of Hilbert modules over locally C *-algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert C *-modules are also valid in the context of Hilbert modules over locally C *-algebras.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Fragoulopoulou: Tensor products of enveloping locally C<Subscript>*</Subscript>-algebras. Schriftenreihe. Univ. Münster, 1997, pp. 1-81.
A. Inoue: Locally C *. Mem. Faculty Sci. Kyushu Univ. Ser. A75 (1971), 197-235.
K. K. Jensen and K. Thomsen: Elements of KK-theory. Birhäuser-Verlag, 1991.
M. Joita: The stabilization theorem for Hilbert modules over locally C *-algebras. The 3rd International Conference on Topological Algebra and Applications, (ICTAA3) Oulu, Finland, July 2-6, 2001.
M. Joita: Strict completely positive linear maps between locally C *-algebras and rep-resentations on Hilbert modules. J. London Math. (2) 66 (2002), 421-432.
E. C. Lance: Hilbert C *-modules. A toolkit for operator algebraists. London Math. Soc. Lecture Note Series 210. Cambridge Univ. Press, Cambridge, 1995.
A. Mallios: Hermitian K-theory over topological *-algebras. J. Math. Anal. Appl. 106 (1985), 454-539.
N. C. Phillips: Inverse limits of C *-algebras. J. Operator Theory 19 (1988), 159-195.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Joiţa, M. Tensor Products of Hilbert Modules Over Locally C *-Algebras. Czechoslovak Mathematical Journal 54, 727–737 (2004). https://doi.org/10.1007/s10587-004-6421-9
Issue Date:
DOI: https://doi.org/10.1007/s10587-004-6421-9