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Local maps and the representation theory of operator algebras


Author: Elias G. Katsoulis
Journal: Trans. Amer. Math. Soc. 368 (2016), 5377-5397
MSC (2010): Primary 46L08, 47B49, 47L40, 47L65
DOI: https://doi.org/10.1090/tran6674
Published electronically: December 14, 2015
MathSciNet review: 3458384
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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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Additional Information

Elias G. Katsoulis
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
Email: katsoulise@ecu.edu

DOI: https://doi.org/10.1090/tran6674
Keywords: Local derivation, local multiplier, reflexivity, topological graph, tensor algebra, $\mathrm{C}^*$-correspondence, Cuntz-Pimsner $\mathrm{C}^*$-algebra.
Received by editor(s): June 11, 2014
Received by editor(s) in revised form: June 19, 2014
Published electronically: December 14, 2015
Article copyright: © Copyright 2015 American Mathematical Society