{"id":10594,"date":"2023-09-21T10:13:36","date_gmt":"2023-09-21T08:13:36","guid":{"rendered":"https:\/\/wpd.ugr.es\/~imag\/?page_id=10594"},"modified":"2023-09-21T10:14:37","modified_gmt":"2023-09-21T08:14:37","slug":"the-robust-and-intriguing-connection-between-banach-space-geometry-and-fixed-point-theory","status":"publish","type":"page","link":"https:\/\/wpd.ugr.es\/~imag\/the-robust-and-intriguing-connection-between-banach-space-geometry-and-fixed-point-theory\/","title":{"rendered":"The robust and intriguing connection between Banach space geometry and fixed-point theory"},"content":{"rendered":"<p><strong>Speaker:<\/strong> M.\u00c1ngeles Jap\u00f3n<\/p>\n<p><strong>Abstract:<\/strong> At first glance, geometry in Banach spaces and metric fixed-point theory seem to be independent areas of research. The goal of this lecture is to expose how these two fields are intrinsically connected. Starting with fixed-point characterizations of weak compactness in different classes of Banach spaces according to their underlying geometry, we will exhibit as particular cases how reflexivity and super-reflexivity can be determined by fixed-point theorems. Finally, we will display some open problems, in particular, whether it is possible to characterize the compact sets $K$  for which the unit ball of \\(C(K)\\) has the fixed-point property. The Stone-Cech compactification for the positive integers \\(\\beta\\mathbb{N}\\) will be our model to claim our conjecture.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: M.\u00c1ngeles Jap\u00f3n Abstract: At first glance, geometry in Banach spaces and metric fixed-point theory seem to be independent areas of research. The goal of this lecture is to expose how these two fields are intrinsically connected. Starting with fixed-point characterizations of weak compactness in different classes of Banach spaces<span class=\"more-link\"><a href=\"https:\/\/wpd.ugr.es\/~imag\/the-robust-and-intriguing-connection-between-banach-space-geometry-and-fixed-point-theory\/\">Continue Reading<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"translation":{"provider":"WPGlobus","version":"3.0.0","language":"en","enabled_languages":["en"],"languages":{"en":{"title":true,"content":true,"excerpt":false}}},"_links":{"self":[{"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/pages\/10594"}],"collection":[{"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/comments?post=10594"}],"version-history":[{"count":3,"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/pages\/10594\/revisions"}],"predecessor-version":[{"id":10596,"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/pages\/10594\/revisions\/10596"}],"wp:attachment":[{"href":"https:\/\/wpd.ugr.es\/~imag\/wp-json\/wp\/v2\/media?parent=10594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}