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Summer 2018 Variant versions of the Lewent type determinantal inequality
Ali Morassaei
Adv. Oper. Theory 3(3): 632-638 (Summer 2018). DOI: 10.15352/aot.1711-1259

Abstract

In this paper, we present a refinement of the Lewent determinantal inequality and show that the following inequality holds $$\det\frac{I_{\mathcal{H}}+A_1}{I_{\mathcal{H}}-A_1}+\det\frac{I_{\mathcal{H}}+A_n}{I_{\mathcal{H}}-A_n}-\sum_{j=1}^n\lambda_j \det\left(\frac{I_{\mathcal{H}}+A_j}{I_{\mathcal{H}}-A_j}\right)$$ $$\ge \det\left[\left(\frac{I_{\mathcal{H}}+A_1}{I_{\mathcal{H}}-A_1}\right)\left(\frac{I_{\mathcal{H}}+A_n}{I_{\mathcal{H}}-A_n}\right)\prod_{j=1}^n \left(\frac{I_{\mathcal{H}}+A_j}{I_{\mathcal{H}}-A_j}\right)^{-\lambda_j}\right],$$ where $A_j\in\mathbb{B}(\mathcal{H})$‎, ‎$0\le A_j < I_\mathcal{H}$‎, ‎$A_j$'s are trace class operators and $A_1 \le A_j \le A_n~(j=1,\ldots,n)$ and $\sum_{j=1}^n\lambda_j=1,‎~ ‎\lambda_j \ge 0‎~ ‎(j=1,\ldots,n)$‎. ‎In addition, we present some new versions of the Lewent type determinantal inequality.

Citation

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Ali Morassaei. "Variant versions of the Lewent type determinantal inequality." Adv. Oper. Theory 3 (3) 632 - 638, Summer 2018. https://doi.org/10.15352/aot.1711-1259

Information

Received: 9 November 2017; Accepted: 25 February 2018; Published: Summer 2018
First available in Project Euclid: 4 April 2018

zbMATH: 06902456
MathSciNet: MR3795104
Digital Object Identifier: 10.15352/aot.1711-1259

Subjects:
Primary: 47B15
Secondary: 15A45, 47A63, 47A64

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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