{"id":26545,"date":"2022-12-30T10:42:22","date_gmt":"2022-12-30T09:42:22","guid":{"rendered":"https:\/\/cio.umh.es\/?p=26545"},"modified":"2023-01-11T14:17:32","modified_gmt":"2023-01-11T13:17:32","slug":"ferrando-j-c-kakol-j-2022-distinguished-vector-valued-continuous-function-spaces-and-injective-tensor-products-bulletin-of-the-belgian-mathematical-society-simon-stevin-28-57-2","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2022\/12\/30\/ferrando-j-c-kakol-j-2022-distinguished-vector-valued-continuous-function-spaces-and-injective-tensor-products-bulletin-of-the-belgian-mathematical-society-simon-stevin-28-57-2\/","title":{"rendered":"Ferrando, J.C., K\u0105kol, J. (2022) "Distinguished vector-valued continuous function spaces and injective tensor products", Bulletin of the Belgian Mathematical Society – Simon Stevin, 28 (5):709\u2013721"},"content":{"rendered":"

Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche) and Jerzy K\u0105kol (Departamento de F\u00edsica Te\u00f3rica, Facultad de Ciencias F\u00edsicas, Universidad Complutense, Madrid)<\/strong><\/p>\n

Abstract:\u00a0<\/strong>The paper continues the study on the distinguished property of the space\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>Cp(X)<\/span><\/span>\u00a0(of real-valued continuous functions over a Tychonoff space\u00a0<\/span>X<\/span><\/span><\/span><\/span>X<\/span><\/span>\u00a0in the pointwise topology) under the formation of tensor products towards the following research directions:\u00a0<\/span>(<\/span><\/span>i<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(i)<\/span><\/span>\u00a0the injective tensor product\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span>\u2297<\/span><\/span><\/span>\u03b5<\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span><\/span><\/span>Cp(X)\u2297\u03b5E<\/span><\/span>\u00a0of\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>Cp(X)<\/span><\/span>\u00a0and a real locally convex space\u00a0<\/span>E<\/span><\/span><\/span><\/span>E<\/span><\/span>\u00a0(and its completion\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span><\/span>\u02c6<\/span><\/span><\/span>\u2297<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b5<\/span><\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span><\/span><\/span>Cp(X)\u2297^\u03b5E<\/span><\/span>), and\u00a0<\/span>(<\/span><\/span>i<\/span><\/span>i<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(ii)<\/span><\/span>\u00a0the space\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>,<\/span><\/span>E<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>Cp(X,E)<\/span><\/span>\u00a0of all\u00a0<\/span>E<\/span><\/span><\/span><\/span>E<\/span><\/span>-valued continuous functions (with a normed space\u00a0<\/span>E<\/span><\/span><\/span><\/span>E<\/span><\/span>) endowed with the pointwise topology. This work leads also to a new characterization of distinguished Fr\u00e9chet locally convex spaces\u00a0<\/span>E<\/span><\/span><\/span><\/span>E<\/span><\/span>. We show, e.g., that if\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span><\/span>Cp(X)<\/span><\/span>\u00a0is metrizable, then\u00a0<\/span>E<\/span><\/span><\/span><\/span>E<\/span><\/span>\u00a0is distinguished if and only if metrizable\u00a0<\/span>C<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>)<\/span><\/span><\/span>\u2297<\/span><\/span><\/span>\u03b5<\/span><\/span><\/span><\/span><\/span><\/span>E<\/span><\/span><\/span><\/span>Cp(X)\u2297\u03b5E<\/span><\/span>\u00a0is distinguished.<\/span><\/p>","protected":false},"excerpt":{"rendered":"

Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche) and Jerzy K\u0105kol (Departamento de F\u00edsica Te\u00f3rica, Facultad de Ciencias F\u00edsicas, Universidad Complutense, Madrid)
\nAbstract:\u00a0The paper continues the study on the distinguished property of the space\u00a0Cp(X)Cp(X)\u00a0(of real-valued continuous functions over a Tychonoff space\u00a0XX\u00a0in the pointwise topology) under the formation of tensor products towards the following […]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","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\/26545"}],"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\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=26545"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26545\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=26545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=26545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=26545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}