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Title: | Properties of cones of nuclear operators working on some separable Hilbert spaces |
Authors: | Mayorga Zambrano, Juan Ricardo Villagómez Chiluisa, Antonio Xavier |
Keywords: | Cono tipo Sobolev Funcional de energía libre Operadores nucleares Sobolev-like cone Free energy functional Nuclear operator |
Issue Date: | Nov-2023 |
Publisher: | Universidad de Investigación de Tecnología Experimental Yachay |
Abstract: | Se definen análogos del espacio de Sobolev H^1 a nivel de operadores nucleares. Estos conjuntos de operadores ya no son espacios lineales normados, sino conos equipados con un concepto de energía total que reemplaza el papel del cuadrado de una norma. Utilizando la Teoría de Operadores, obtenemos propiedades similares a las obtenidas por Mayorga et al. cuando el espacio pivote L^2 (R^N ) se reemplaza por otro espacio de Hilbert separable, como H^1 (R^N ), con N > 4. El trabajo está relacionado con la estabilidad de sistemas cuánticos (representada por los operadores nucleares) y por ello, también se estudian propiedades de funcionales de energía libre definidos sobre el cono de operadores. En este contexto, se prueban desigualdades tipo Gagliardo-Nirenberg para operadores. |
Description: | Analogues of the Sobolev space H^1 are defined at the level of nuclear operators. These sets of operators are no longer normed linear spaces but cones equipped with a concept of total energy that replaces the role of the square of a norm. Using Operator Theory, we obtain properties similar to those obtained by Mayorga et al. when the pivot space L^2 (R^N ) is replaced by another separable Hilbert space, such as H^1 (R^N ), with N > 4. The work is related to the stability of quantum systems (represented by nuclear operators), and therefore, properties of free energy functionals defined on the operator cone are also studied. In this context, Gagliardo-Nirenberg type inequalities for operators are proven. |
URI: | http://repositorio.yachaytech.edu.ec/handle/123456789/672 |
Appears in Collections: | Matemática |
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ECMC0135.pdf | 716.35 kB | Adobe PDF | View/Open |
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