Nuclear and type I C*-crossed products
We prove that a C*-crossed product A ×α G by a locally compact group G is nuclear (respectively type I or liminal) if and only if certain hereditary C*-subalgebras, Sπ, Iπ ⊂ A ×α G π , are nuclear (respectively type I or liminal). Analog characterizations are proved for C*-crossed products by compact quantum groups. These subalgebras are the analogs of the algebras of spherical functions considered by R. Godement for groups with large compact subgroups. If K = G is a compact group or a compact quantum group, the algebras Sn are stably isomorphic with the fixed point algebras A ⊗ B(Hπ)α⊗adπ where Hπ is the Hilbert space of the representation π. © Theta, 2013.
Journal of Operator Theory
Digital Object Identifier (DOI)
Dumitru, & Peligrad, C. (2013). NUCLEAR AND TYPE I C-CROSSED PRODUCTS. Journal of Operator Theory, 69(1), 287–296. https://doi.org/10.7900/jot.2010dec08.1907