{"id":86418,"date":"2018-03-10T00:10:58","date_gmt":"2018-03-10T00:10:58","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/universaliad-hiperciclicidad-y-caos-en-espacios-de-frechet\/"},"modified":"2018-03-10T00:10:58","modified_gmt":"2018-03-10T00:10:58","slug":"universaliad-hiperciclicidad-y-caos-en-espacios-de-frechet","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/universaliad-hiperciclicidad-y-caos-en-espacios-de-frechet\/","title":{"rendered":"Universaliad, hiperciclicidad y caos en espacios de fr\u00e9chet"},"content":{"rendered":"<h2>Tesis doctoral de <strong> F\u00e9lix Mart\u00ednez Gimenez <\/strong><\/h2>\n<p>El objetivo de esta tesis es el estudio de la hiperciclicidad y el caos en espacios de fr\u00e9chet. Concretamente se abordan las siguientes cuestiones:  estudio de la hiperciclicidad y el caos de operadores backward shift ponderados en espacios escalonados de k\u00ed\u00b6the. Se obtienen caracterizaciones haciendo uso de diagramas conmutativos y de un lema de comparaci\u00f3n que generaliza l principio de comparaci\u00f3n de hiperciclicidad de shapiro. Se prueban tambi\u00e9n resultados sobre la hiperciclicidad y el caos de perturbaciones de la identidad por operadores backward shift.  estudio de la existencia de operadores ca\u00f3ticos en espacios de fr\u00e9chet separables de dimensi\u00f3n infinita. Se presenta un ejemplo de espacio de banach separable de dimensi\u00f3n infinita que no admite ning\u00fan operador ca\u00f3tico. la demostraci\u00f3n depende de resultados profundos en la teor\u00eda de espacios de banach; se utilizan, por primera vez en este contexto,los espacios de bahacj complejos hereditariamente indescomponibles recientemente obtenidos por gowers y maurey.  estudio de la incidencia de los productos tensoriales en la hiperciclicidad y el caos. Los resultados probados se pueden aplicar al estudio de la hiperciclicidad de operadores en espacios de funciones de varias variables. Tambi\u00e9n se estudia la universalidad de operadores de composici\u00f3n en distintas \u00e1lgebras de operadores y como consecuencia se dan condiciones de existencia de subespacios cerrados de vectores universales.  estudio de la hiperciclicidad y el caos de ciertos polinomios (uno homog\u00e9neo y otro no homog\u00e9neo) en espacios de fr\u00e9chet. Concretamente se caracteriza el caos de un polinomio $d$-homog\u00e9neo ($d\/ge2$) y se dan condiciones suficientes de hiperciclicidad y caos de un polinomio no-homog\u00e9neo, en ambos casos definidos en espacios escalonados de k\u00ed\u00b6the.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Universaliad, hiperciclicidad y caos en espacios de fr\u00e9chet<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Universaliad, hiperciclicidad y caos en espacios de fr\u00e9chet <\/li>\n<li><strong>Autor:<\/strong>\u00a0 F\u00e9lix Mart\u00ednez Gimenez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Valencia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 18\/09\/2000<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Alfredo Peris Manguillot<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: manuel Valdivia ure\u00f1a <\/li>\n<li>Antonio Bonilla ramirez (vocal)<\/li>\n<li>Luis Bernal gonz\u00e1lez (vocal)<\/li>\n<li>Antonio Galbis verd\u00fa (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de F\u00e9lix Mart\u00ednez Gimenez El objetivo de esta tesis es el estudio de la hiperciclicidad y el caos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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