{"id":2160,"date":"2012-06-20T23:22:41","date_gmt":"2012-06-20T15:22:41","guid":{"rendered":"http:\/\/vanabel.sinaapp.com\/?p=2160"},"modified":"2012-06-20T23:22:41","modified_gmt":"2012-06-20T15:22:41","slug":"%e8%a5%bf%e5%a4%a72007%e6%b3%9b%e5%87%bd%e5%88%86%e6%9e%90%e7%a0%94%e7%a9%b6%e7%94%9f%e8%af%95%e9%a2%98","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=2160","title":{"rendered":"\u897f\u59272007\u6cdb\u51fd\u5206\u6790(\u7814\u7a76\u751f)\u8bd5\u9898"},"content":{"rendered":"<ol>\n<li>\u53d9\u8ff0\u5b9a\u4e49: \u51f8\u96c6, \u5747\u8861\u96c6, \u6709\u754c\u96c6, \u5438\u6536\u96c6, \u8c31.<\/li>\n<li>\u8bbe $\\beta$ \u4e3a\u62d3\u6251\u5411\u91cf\u7a7a\u95f4 $X$ \u7684\u5c40\u90e8\u57fa, \u5219 $\\beta$ \u4e2d\u7684\u6bcf\u4e00\u5143\u90fd\u5305\u542b\u67d0\u4e00\u4e2a\u5143\u7684\u95ed\u5305.<\/li>\n<li>\u8bbe $X$ \u4e3a\u65e0\u7a77\u7ef4\u62d3\u6251\u5411\u91cf\u7a7a\u95f4, \u5b83\u662f\u53ef\u6570\u591a\u4e2a\u6709\u9650\u7ef4\u5b50\u7a7a\u95f4\u7684\u5e76, \u8bc1\u660e: $X$ \u5728\u81ea\u8eab\u662f\u7b2c\u4e00\u7eb2\u96c6.<\/li>\n<p><!--more--><\/p>\n<li>\u8bbe $X$ \u662f\u62d3\u6251\u5411\u91cf\u7a7a\u95f4, $f$ \u4e3a $X$ \u4e0a\u7684\u975e\u5e38\u503c\u7684\u7ebf\u6027\u6cdb\u51fd, \u5219 $f$ \u5fc5\u4e3a\u5f00\u6620\u5c04.<\/li>\n<li>\u8bbe $X$ \u4e3a\u5c40\u90e8\u51f8\u7a7a\u95f4, $K$ \u4e3a $X$ \u7684\u51f8\u5b50\u96c6, \u8bd5\u8bc1: $\\bar K^w=\\bar K$.<\/li>\n<li>\u8bbe $X$ \u4e3a\u81ea\u53cd\u7684 Banach \u7a7a\u95f4, \u8bc1\u660e\u5bf9\u4efb\u4e00 $f\\in X^\\ast$, $|f(x)|$ \u5728 $X$ \u7684\u5355\u4f4d\u7403\u9762\u4e0a\u53ef\u53d6\u5f97\u6700\u5927\u503c.<\/li>\n<li>\u5982\u679c $X$ \u662f\u7d27\u81f4\u7684\u62d3\u6251\u5411\u91cf\u7a7a\u95f4, $\\set{f_n}$ \u662f $X$ \u4e0a\u53ef\u5206\u70b9\u7684\u8fde\u7eed\u5b9e\u503c\u51fd\u6570\u5217, \u5219 $X$ \u662f\u53ef\u5ea6\u91cf\u5316\u7684.<\/li>\n<li>\u8bbe $X$ \u662f Banach \u7a7a\u95f4, \u5982\u679c $T\\in\\beta(X)$, $\\lambda\\neq0$, \u4e14 $T$ \u662f\u7d27\u7b97\u5b50, \u5219 $\\rm{dim} N(T-\\lambda T)$ .<\/li>\n<li>\u8bbe $X$ \u662f Banach \u7a7a\u95f4, \u5982\u679c $T\\in\\beta(X)$, \u8bc1\u660e $T$ \u4e3a\u6709\u754c\u7ebf\u6027\u7b97\u5b50\u7684\u5145\u8981\u6761\u4ef6\u662f\u5bf9\u4efb\u610f\u7684 $x_n$ \u5f31\u6536\u655b\u5230 $x$, \u90fd\u6709 $Tx_n$ \u5f31\u6536\u655b\u4e8e $Tx$.<\/li>\n<li>\u8bbe $X$ \u662f Banach \u7a7a\u95f4, $B$ \u4e3a $X$ \u4e2d\u7684\u95ed\u5355\u4f4d\u7403, \u8bd5\u8bc1: $X$ \u81ea\u53cd\u5f53\u4e14\u4ec5\u5f53 $B$ \u662f\u5f31\u7d27\u7684.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u53d9\u8ff0\u5b9a\u4e49: \u51f8\u96c6, \u5747\u8861\u96c6, \u6709\u754c\u96c6, \u5438\u6536\u96c6, \u8c31. \u8bbe $\\beta$ \u4e3a\u62d3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/lttt.vanabel.cn\/?p=2160\"> <span class=\"screen-reader-text\">\u897f\u59272007\u6cdb\u51fd\u5206\u6790(\u7814\u7a76\u751f)\u8bd5\u9898<\/span> \u9605\u8bfb\u66f4\u591a &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[800,746,390,418],"class_list":["post-2160","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-lecture-notes","tag-746","tag-390","tag-418"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/2160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2160"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/2160\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}