Trace-class operators on Hilbert modules and Haagerup tensor products
| Autor: | Crisp, Tyrone, Rosbotham, Michael |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that the space of trace-class operators on a Hilbert module over a commutative C*-algebra, as defined and studied in earlier work of Stern and van Suijlekom (Journal of Functional Analysis, 2021), is completely isometrically isomorphic to a Haagerup tensor product of the module with its operator-theoretic adjoint. This generalises a well-known property of Hilbert spaces. In the course of proving this, we also obtain a new proof of a result of Stern-van Suijlekom concerning the equivalence between two definitions of trace-class operators on Hilbert modules. Comment: 13 pages |
| Databáze: | arXiv |
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