{"title":"关于闭合凸锥上的CCR和CAR流的注释","authors":"Anbu Arjunan","doi":"10.1142/s0219025721500211","DOIUrl":null,"url":null,"abstract":"For a closed convex cone <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> in <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> which is spanning and pointed, i.e. <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">−</mml:mo> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi> <mml:mo stretchy=\"false\">∩</mml:mo><mml:mo stretchy=\"false\">−</mml:mo><mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">}</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> we consider a family of <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>-semigroups over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> consisting of a certain family of CCR flows and CAR flows over <inline-formula><mml:math display=\"inline\" overflow=\"scroll\"><mml:mi>P</mml:mi></mml:math></inline-formula> and classify them up to the cocycle conjugacy.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on CCR and CAR flows over closed convex cones\",\"authors\":\"Anbu Arjunan\",\"doi\":\"10.1142/s0219025721500211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a closed convex cone <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> in <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> which is spanning and pointed, i.e. <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi> <mml:mo stretchy=\\\"false\\\">−</mml:mo> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi> <mml:mo stretchy=\\\"false\\\">∩</mml:mo><mml:mo stretchy=\\\"false\\\">−</mml:mo><mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\\\"false\\\">{</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\\\"false\\\">}</mml:mo><mml:mo>,</mml:mo></mml:math></inline-formula> we consider a family of <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>-semigroups over <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> consisting of a certain family of CCR flows and CAR flows over <inline-formula><mml:math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mml:mi>P</mml:mi></mml:math></inline-formula> and classify them up to the cocycle conjugacy.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219025721500211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219025721500211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Remarks on CCR and CAR flows over closed convex cones
For a closed convex cone P in ℝd which is spanning and pointed, i.e. P−P=ℝd and P∩−P={0}, we consider a family of E0-semigroups over P consisting of a certain family of CCR flows and CAR flows over P and classify them up to the cocycle conjugacy.