Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896686 | Journal of Functional Analysis | 2018 | 25 Pages |
Abstract
A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a tracial state, we give a different proof. We also improve and generalize to the setting of finite von Neumann algebras, some 'Fischer-type' inequalities by Matic for determinants of perturbed positive-definite matrices. In the process, a conceptual framework is established for viewing these inequalities as manifestations of Jensen's inequality in conjunction with the theory of operator monotone and operator convex functions on [0,â). We place emphasis on documenting necessary and sufficient conditions for equality to hold.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Soumyashant Nayak,