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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.

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Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Morassaei, Ali - 

Id.: 71252699

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveLewent inequality‎ - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 Tusi Mathematical Research Group

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 2538-225X

Fecha de contribución: 28-abr-2018

Contacto:

Localización:
* doi:10.15352/aot.1711-1259

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