Geodesic
Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras
Documenta mathematica, Tome 30 (2025) no. 4, pp. 909-933

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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 
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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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