Abstract
In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical system. We describe how these crossed product constructions behave under G-equivariant maps, tensor products, and the canonical C⁎-covers. We show that hyperrigidity is preserved under two of the three crossed products. Finally, using A. Kavruk's notion of an operator system that detects C⁎-nuclearity, we give a negative answer to a question on operator algebra crossed products posed by Katsoulis and Ramsey.
Original language | English (US) |
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Pages (from-to) | 2156-2193 |
Number of pages | 38 |
Journal | Journal of Functional Analysis |
Volume | 276 |
Issue number | 7 |
DOIs | |
State | Published - Apr 1 2019 |
Externally published | Yes |
Keywords
- Crossed products
- Nuclearity
- Operator algebras
- Operator systems
ASJC Scopus subject areas
- Analysis