Local maps and the representation theory of operator algebras

Katsoulis, Elias

doi:10.1090/tran6674

Local maps and the representation theory of operator algebras
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by Elias G. Katsoulis PDF

Trans. Amer. Math. Soc. 368 (2016), 5377-5397 Request permission

Abstract:

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an automorphic semicrossed product $C(\Omega ) \times _{\sigma } \mathbb {Z}^{+}$ is a derivation (resp. left multiplier). In the process we obtain various results of independent interest. In particular, we show that the finite dimensional nest representations of the tensor algebra of a topological graph separate points.

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