Taiwanese Journal of Mathematics

A LEWENT TYPE DETERMINANTAL INEQUALITY

Minghua Lin

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Abstract

We prove a Lewent type determinantal inequality: Let $A_i$, $i=1,\ldots, n$, be (strictly) contractive trace class operators over a separable Hilbert space. Then \[ \left|\det\left(\frac{I+\displaystyle\sum_{i=1}^n\lambda_iA_i}{I-\displaystyle\sum_{i=1}^n\lambda_iA_i}\right)\right|\le\prod_{i=1}^n\det\left(\frac{I+|A_i|}{I-|A_i|}\right)^{\lambda_i}, \] where $\sum_{i=1}^n \lambda_i = 1$, $\lambda_i \ge 0$, $i=1,\ldots, n$, are (scalar) weights and $|A| = (A^*A)^{1/2}$.

Article information

Source
Taiwanese J. Math., Volume 17, Number 4 (2013), 1303-1309.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706118

Digital Object Identifier
doi:10.11650/tjm.17.2013.2682

Mathematical Reviews number (MathSciNet)
MR3085512

Zentralblatt MATH identifier
1300.47028

Subjects
Primary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 15A45: Miscellaneous inequalities involving matrices

Keywords
Lewent inequality determinantal inequality trace class operators contraction

Citation

Lin, Minghua. A LEWENT TYPE DETERMINANTAL INEQUALITY. Taiwanese J. Math. 17 (2013), no. 4, 1303--1309. doi:10.11650/tjm.17.2013.2682. https://projecteuclid.org/euclid.twjm/1499706118


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