{"id":15414,"date":"2002-01-02T00:00:00","date_gmt":"2002-01-02T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/contribuciones-a-la-teroria-de-jb-algebras-no-conmutativas-y-de-c-algebras-alternativas\/"},"modified":"2002-01-02T00:00:00","modified_gmt":"2002-01-02T00:00:00","slug":"contribuciones-a-la-teroria-de-jb-algebras-no-conmutativas-y-de-c-algebras-alternativas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/contribuciones-a-la-teroria-de-jb-algebras-no-conmutativas-y-de-c-algebras-alternativas\/","title":{"rendered":"Contribuciones a la teroria de jb*-algebras no -conmutativas y de c*-algebras alternativas."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Antonio Morales Campoy <\/strong><\/h2>\n<p>En este trabajo se abordan diferentes aspectos de la teoria de las c*-algebras no-asociativas (es decir,no necesariamente asociativas). La teoria de c*-algebras (asociativas) fue introducida en 1943 por gelfand y naimark, al caracterizar abstractamente las sub\u00e1lgebras cerradas y autoadjuntas de las \u00e1lgebras de operadores lineales y acotados sobre un espacio de hilbert complejo. la consideraci\u00f3n de la axiomaticas de gelfand-naimark y vidav-palmer un ambiente no-asociativo da lugar a las c*-albegras no-asociativas, a saber, las c*-\u00e1lgebras alternativas y las jb*-algebras no-conmutativas. Las c*-algebras alternativas (respectivamente, las jb*-algebras no-conmutativas) con unidad no son m\u00e1s que las algebras complejas no-asociativas normadas completas con unidad de norma uno que verifican el axioma de gelfand-naimark(respectivamente, vidav-palmer). Dado que el axioma de gelfand-naimark implica el axioma de vidav-palmer (pero no al reves), toda c*-\u00e1lgebra alternativa es una jb*-\u00e1lgebra no -conmutativa.  el capitulo 2 se dedica al estudio de ciertas propiedades geometricas de los productos de las c*-algebras no-asociativas. Inspir\u00e1ndose en el teorema de bohnenblust-karlin, se prueba (corolario ii.3.6) que el producto en una c*-\u00e1lgebra alternativa a es un v\u00e9rtice de la bola unidad cerrada del espacio de banach de todas las aplicaciones bilineales continuas de a x a en a(como consecuencia de que el indice numerico es igual a 1 o 1\/2 seg\u00fan que a sea o no conmutativa, teorema ii.3.5). Dicho resultado era desconocido incluso en el caso asociativo. Se demuestra en el ejemplo ii.4.1 que tal resultado no cabe esperarlo en el caso de las jb*-\u00e1lgebras.  la clasificaci\u00f3n de las jb*-\u00e1lgebras no-conmutativas primas es el principal resultado del capitulo 3. Seg\u00fan el teorema el teorema ii.2.5 estas son conmutativas, o cuadraticas o la mutaci\u00f3n de c*-algebras primas para un real en ]1\/2,1], todas ellas bien conocidas. Dicho resultado extiende la<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Contribuciones a la teroria de jb*-algebras no -conmutativas y de c*-algebras alternativas.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Contribuciones a la teroria de jb*-algebras no -conmutativas y de c*-algebras alternativas. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Antonio Morales Campoy <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Almer\u00eda<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/02\/2002<\/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>Amin Kaidi Lhachmi<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Isidro gomez Jos\u00e9 Mar\u00eda <\/li>\n<li>Antonio Fernandez lopez (vocal)<\/li>\n<li>pere Ara bertran (vocal)<\/li>\n<li>Antonio Moreno galindo (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Antonio Morales Campoy En este trabajo se abordan diferentes aspectos de la teoria de las c*-algebras no-asociativas [&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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