{"id":468,"date":"2025-07-17T14:54:23","date_gmt":"2025-07-17T13:54:23","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=468"},"modified":"2025-07-18T09:34:39","modified_gmt":"2025-07-18T08:34:39","slug":"rang-real-zero-per-algebres-doperadors","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/rang-real-zero-per-algebres-doperadors\/","title":{"rendered":"Rang real zero per \u00e0lgebres d&#8217;operadors"},"content":{"rendered":"\n<p>Una C*-\u00e0lgebra \u00e9s una \u00e0lgebra de Banach (normada) complexa amb involuci\u00f3 que satisf\u00e0 l&#8217;equaci\u00f3 \\(\\Vert aa^*\\Vert = \\Vert a\\Vert\\). Els examples cl\u00e0ssics s\u00f3n, en el cas commutatiu, \\(C(X)\\), funcions cont\u00ednues amb valors complexos sobre un espai compacte Hausdorff, productes finits de matrius sobre els complexos o, m\u00e9s en general, l&#8217;\u00e0lgebra d&#8217;operadors lineals continus sobre un espai de Hilbert separable.<\/p>\n<p>Despr\u00e9s d&#8217;establir un toolkit per poder treballar amb aquests objectes, el treball proposa explorar la noci\u00f3 de rang real zero com a dimensi\u00f3 no commutativa, estudiar qu\u00e8 vol dir en el cas commutatiu, i establir diverses propietats de perman\u00e8ncia, com per exemple el pas a matrius i a l\u00edmits inductius. Totes aquestes propietats van estar provades a l&#8217;article fundacional de Brown i Pedersen el 1991. Si el temps ho permet, s&#8217;abordar\u00e0 l&#8217;estudi de les conjectures de Brown i Pedersen, que han estat refutades recentment.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Una C*-\u00e0lgebra \u00e9s una \u00e0lgebra de Banach (normada) complexa amb involuci\u00f3 que satisf\u00e0 l&#8217;equaci\u00f3 \\(\\Vert aa^*\\Vert = \\Vert a\\Vert\\). Els examples cl\u00e0ssics s\u00f3n, en el cas commutatiu, \\(C(X)\\), funcions cont\u00ednues amb valors complexos sobre un espai compacte Hausdorff, productes finits de matrius sobre els complexos o, m\u00e9s en general, l&#8217;\u00e0lgebra d&#8217;operadors lineals continus sobre un [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29],"tags":[46],"class_list":["post-468","post","type-post","status-publish","format-standard","hentry","category-algebra","category-analisi-matematica","tag-francesc-perera"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/468","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=468"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/468\/revisions"}],"predecessor-version":[{"id":471,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/468\/revisions\/471"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}