{"id":573,"date":"2025-07-27T18:37:51","date_gmt":"2025-07-27T17:37:51","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=573"},"modified":"2025-07-28T20:37:55","modified_gmt":"2025-07-28T19:37:55","slug":"573-2","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/573-2\/","title":{"rendered":"El problema de matrius complexes de Halmos"},"content":{"rendered":"\n<p>Un problema atribu\u00eft a von Neumann i que va ser popularitzat per Halmos el 1976 pregunta si donades dues matrius complexes herm\u00edtiques \\(A,B\\in M_n(\\mathbb{C})\\) (o sigui, iguals a les seves conjugades-transposades) tals que \\(\\Vert AB-BA\\Vert\\) \u00e9s petita poden ser perturbades lleugerament per aconseguir matrius herm\u00edtiques \\(A&#8217;,B&#8217;\\) tals que \\(A&#8217;B&#8217;=B&#8217;A&#8217;\\). Halmos tamb\u00e9 va fer la mateixa pregunta per matrius unit\u00e0ries (\u00e9s a dir, invertibles amb inversa la transposada-conjugada). La naturalesa aparentment innocent d&#8217;aquestes preguntes amaga aspectes anal\u00edtics, algebraics, i de grups de cohomologia. L&#8217;objectiu del treball \u00e9s analitzar les respostes donades a aquestes preguntes (algunes negatives, altres positives). Tamb\u00e9 s&#8217;analitzaran, com a ampliaci\u00f3 natural, els anells anomenats estables per la norma.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un problema atribu\u00eft a von Neumann i que va ser popularitzat per Halmos el 1976 pregunta si donades dues matrius complexes herm\u00edtiques \\(A,B\\in M_n(\\mathbb{C})\\) (o sigui, iguals a les seves conjugades-transposades) tals que \\(\\Vert AB-BA\\Vert\\) \u00e9s petita poden ser perturbades lleugerament per aconseguir matrius herm\u00edtiques \\(A&#8217;,B&#8217;\\) tals que \\(A&#8217;B&#8217;=B&#8217;A&#8217;\\). Halmos tamb\u00e9 va fer la mateixa [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29,31],"tags":[46],"class_list":["post-573","post","type-post","status-publish","format-standard","hentry","category-algebra","category-analisi-matematica","category-geometria-i-topologia","tag-francesc-perera"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/573","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=573"}],"version-history":[{"count":4,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/573\/revisions"}],"predecessor-version":[{"id":578,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/573\/revisions\/578"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}