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2013 A LEWENT TYPE DETERMINANTAL INEQUALITY
Minghua Lin
Taiwanese J. Math. 17(4): 1303-1309 (2013). DOI: 10.11650/tjm.17.2013.2682

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 $|A| = (A^*A)^{1/2}$.

Citation

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Minghua Lin. "A LEWENT TYPE DETERMINANTAL INEQUALITY." Taiwanese J. Math. 17 (4) 1303 - 1309, 2013. https://doi.org/10.11650/tjm.17.2013.2682

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1300.47028
MathSciNet: MR3085512
Digital Object Identifier: 10.11650/tjm.17.2013.2682

Subjects:
Primary: 15A45, 47B15

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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