Geodesic
Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras
Adam Humeniuk1 ; Elias G. Katsoulis2 orcid ; Christopher Ramsey3
1Mount Royal University, Calgary, AB, Canada
2East Carolina University, Greenville, USA
3MacEwan University, Edmonton, AB, Canada
Documenta mathematica, Tome 30 (2025) no. 4, pp. 909-933

Voir la notice de l'article provenant de la source EMS Press

In this paper, we show that the semi-Dirichlet C∗-covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet C∗-cover. Given an operator algebra dynamical system we prove a dilation theory that shows that the full crossed product is isomorphic to the relative full crossed product with respect to this maximal semi-Dirichlet cover. In this way, we can show that every semi-Dirichlet dynamical system has a semi-Dirichlet full crossed product.
DOI : 10.4171/dm/1007
Classification : 47L40, 46L05, 46L07, 47L55, 47L65
Mots-clés : Dirichlet, semi-Dirichlet, C∗-cover, operator algebra, non-selfadjoint

Adam Humeniuk  1   ; Elias G. Katsoulis  2   ; Christopher Ramsey  3

1 Mount Royal University, Calgary, AB, Canada
2 East Carolina University, Greenville, USA
3 MacEwan University, Edmonton, AB, Canada 
Adam Humeniuk; Elias G. Katsoulis; Christopher Ramsey. Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras. Documenta mathematica, Tome 30 (2025) no. 4, pp. 909-933. doi: 10.4171/dm/1007
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