Geodesic
Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 550-563

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we propose a new technical tool for analyzing representations of Hilbert ${{C}^{*}}$ - product systems. Using this tool, we give a new proof that every doubly commuting representation over ${{\mathbb{N}}^{k}}$ has a regular isometric dilation, and we also prove sufficient conditions for the existence of a regular isometric dilation of representations over more general subsemigroups of $\mathbb{R}_{+}^{k}$ .
DOI : 10.4153/CMB-2010-060-8
Mots-clés : 47A20, 46L08 
Shalit, Orr Moshe. Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 550-563. doi: 10.4153/CMB-2010-060-8
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-060-8/}
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[1] [1] Arveson, W., Noncommutative dynamics and E-semigroups. Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. Google Scholar

[2] [2] Lance, E. C., Hilbert C*-modules. A toolkit for operator algebraists. London Mathematical Society Lecture Note Series, 210, Cambridge University Press, Cambridge, 1995. Google Scholar

[3] [3] Fowler, N. J., Discrete product systems of Hilbert bimodules. Pacific J. Math. 204, no. 2 (2002), 335–375. doi:10.2140/pjm.2002.204.335 Google Scholar

[4] [4] Muhly, P. and Solel, B., Tensor algebras over C*-correspondences: representations, dilations, and C*-envelopes. J. Funct. Anal. 158(1998), no. 2, 389–457. doi:10.1006/jfan.1998.3294 Google Scholar

[5] [5] Muhly, P. and Solel, B., Quantum Markov processes (Correspondences and Dilations). Internat. J. Math. 13(2002), no. 8, 863–906. doi:10.1142/S0129167X02001514 Google Scholar

[6] [6] Shalit, O. M., Dilation theorems for contractive semigroups., 2007, Google Scholar | arXiv

[7] [7] Shalit, O. M., E -dilation of strongly commuting CP -semigroups.. J. Funct. Anal. 255(2008), no. 1, 46–89. doi:10.1016/j.jfa.2008.04.003 Google Scholar

[8] [8] Skeide, M., Product Systems; a Survey with commutants in view. In: Quantum stochastics and information, World Sci. Publ., Hackensack, NJ, 2008. Google Scholar

[9] [9] Solel, B., Regular dilations of representations of product systems. Math. Proc. R. Ir. Acad. 108(2008), no. 1, 89–110. doi:10.3318/PRIA.2008.108.1.89 Google Scholar

[10] [10] Sekefal’vi-Nad’, B. and Fojaş, C., Harmonic analysis of operators in Hilbert space. Izdat “Mir”, Moscow, 1970. Google Scholar

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