A note on the positivity of inverse operators acting on C⋆-algebras
For a positive and invertible linear operator T acting on a C ⋆ -algebra, we give necessary and sufficient criteria for the inverse operator T − 1 to be positive, too. Moreover, a simple counterexample shows that T − 1 need not be positive even if T is unital and its spectrum is contained in the unit circle.
Authors
- Jochen Glück (ORCID: https://orcid.org/0000-0002-0319-6913)
- Ulrich Groh
Institutions
- University of Wuppertal (DE)
- University of Tübingen (DE)
Publication Details
- Journal
- Linear Algebra and its Applications
- Published
- 2024-12-16
- DOI
- https://doi.org/10.1016/j.laa.2024.12.006
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00