Crossed products and C* -covers of semi-Dirichlet operator algebras
Faculty Advisor
Date
2025
Keywords
Dirichlet, semi-Dirichlet, C∗-cover, operator algebra, non-selfadjoint
Abstract (summary)
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.
Publication Information
Humeniuk, A., Katsoulis, E., & Ramsey, C. (2025). Crossed products and C* -covers of semi-Dirichlet operator algebras. Documenta Mathematica, 30(4), 909-933. https://doi.org/10.4171/dm/1007
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