Journal of Operator Theory

Volume 95, Issue 1, Winter 2026 pp. 223-245.

Admissibility of $C^*$-covers for operator algebra dynamical systems

Authors: Mitch Hamidi
Author institution: Department of Mathematics, Embry-Riddle Aeronautical University, Prescott, AZ 86301-3720, U.S.A.

Summary: We characterize when a $C^*$-cover admits a $C^*$-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the $C^*$-covers that admit such an extension form a complete lattice. We study dynamical systems arising from groups acting via inner automorphisms in a $C^*$-cover and produce an example of a $C^*$-cover that admits no extension of dynamics on a finite-dimensional non-self-adjoint operator algebra. We construct a partial action on a class of $C^*$-covers that recovers the crossed product of an operator algebra as a subalgebra of the partial crossed product, even when the $C^*$-cover admits no dynamical extension.

DOI: http://dx.doi.org/10.7900/jot.2024apr30.2466
Keywords: $\alpha$-admissibility, $C^*$-cover, crossed product, operator algebra, non-selfadjoint

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