Bounds for Relative Entropic Normalized Determinant of Positive Operators in Hilbert Spaces Via Kantorovich Ratio
Abstract
For positive invertible operators $A$, $B$ and $x\in H$ with $\left\Vert x\right\Vert =1$ we define the relative entropic normalized determinant $D_{x}\left( A|B\right) $ by \begin{equation*} D_{x}\left( A|B\right) :=\exp \left\langle A^{\frac{1}{2}}\left( \ln \left( A^{-\frac{1}{2}}BA^{-\frac{1}{2}}\right) \right) A^{\frac{1}{2}% }x,x\right\rangle . \end{equation*} In this paper we show, among others, that, if the positive invertible operators $A$, $B$ satisfy the condition $0
Fields of Study & Subjects
Mathematical Inequalities and Applications
Matrix Theory and Algorithms
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Journal of Operator Theory and Inequalities
- Volume
- 1
- Issue
- 1
- Pages
- 1–13
- Publication date
- 6 February 2026
- Language
- EN