{"id":12322,"date":"2018-12-07T12:40:34","date_gmt":"2018-12-07T12:40:34","guid":{"rendered":"http:\/\/cio.edu.umh.es\/?p=12322"},"modified":"2018-12-07T12:40:34","modified_gmt":"2018-12-07T12:40:34","slug":"weak-compactness-and-metrizability-of-mackey-bounded-sets-in-frechet-spaces-2018-akademiai-kiado-1-15","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2018\/12\/07\/weak-compactness-and-metrizability-of-mackey-bounded-sets-in-frechet-spaces-2018-akademiai-kiado-1-15\/","title":{"rendered":"Weak compactness and metrizability of Mackey*-bounded sets in Fr\u00e9chet spaces (2018). Akad\u00e9miai Kiad\u00f3, 1-15."},"content":{"rendered":"<p>[:es]<strong>Juan Carlos Ferrando<\/strong>\u00a0(<em>University Miguel Hernandez of Elche<\/em>) and\u00a0<strong>Jerzy K\u0105kol<\/strong>\u00a0(<em>University\u00a0<\/em><em>Adam Mickiewicz of Pozna\u0144<\/em>).<br \/>\n<strong>Abstract.<\/strong>\u00a0Motivated by the density condition in the sense of Heinrich for Fr\u00e9chet spaces and by some results of Schl\u00fcchtermann and Wheeler for Banach spaces, we characterize in terms of certain weakly compact resolutions those Fr\u00e9chet spaces enjoying the property that each bounded subset of its Mackey* dual is metrizable. We also characterize those K\u00f6the echelon Fr\u00e9chet spaces\u00a0\u03bbp(A) as well as\u00a0those Fr\u00e9chet spaces\u00a0<em class=\"EmphasisTypeItalic\">C<\/em><sub><em class=\"EmphasisTypeItalic\">k<\/em><\/sub>\u00a0(<em class=\"EmphasisTypeItalic\">X<\/em>) of real-valued continuous functions equipped with the compact-open topology that enjoy this property.<br \/>\n<strong>Keywords. <\/strong>Bounded resolution; weakly compact resolution;\u00a0G-base of neighborhoods; K-analytic space; SWKA space; SWCG space[:]<\/p>","protected":false},"excerpt":{"rendered":"<p>[:es]Juan Carlos Ferrando\u00a0(University Miguel Hernandez of Elche) and\u00a0Jerzy K\u0105kol\u00a0(University\u00a0Adam Mickiewicz of Pozna\u0144).<br \/>\nAbstract.\u00a0Motivated by the density condition in the sense of Heinrich for Fr\u00e9chet spaces and by some results of Schl\u00fcchtermann and Wheeler for Banach spaces, we characterize in terms of certain weakly compact resolutions those Fr\u00e9chet spaces enjoying the property that each bounded subset of [&#8230;]<\/p>","protected":false},"author":3477,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/12322"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/3477"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=12322"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/12322\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=12322"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=12322"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=12322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}