Crossed products of operator systems

Samuel J. Harris, Se Jin Kim

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish (US)
Pages (from-to)2156-2193
Number of pages38
JournalJournal of Functional Analysis
Volume276
Issue number7
DOIs
StatePublished - Apr 1 2019
Externally publishedYes

Keywords

  • Crossed products
  • Nuclearity
  • Operator algebras
  • Operator systems

ASJC Scopus subject areas

  • Analysis

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