Trace-class operators on Hilbert modules and Haagerup tensor products
Abstract
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.
Fields of Study & Subjects
Advanced Topics in Algebra
Spectral Theory in Mathematical Physics
Advanced Operator Algebra Research
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 95
- Issue
- 2
- Pages
- 519–535
- Publication date
- 30 April 2026
- Language
- EN