Local maps and the representation theory of operator algebras
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- by Elias G. Katsoulis PDF
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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.References
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Additional Information
- Elias G. Katsoulis
- Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
- MR Author ID: 99165
- Email: katsoulise@ecu.edu
- Received by editor(s): June 11, 2014
- Received by editor(s) in revised form: June 19, 2014
- Published electronically: December 14, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5377-5397
- MSC (2010): Primary 46L08, 47B49, 47L40, 47L65
- DOI: https://doi.org/10.1090/tran6674
- MathSciNet review: 3458384