We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of “E$^*$-algebras that are pre-C$^*$-algebras” in the sense of Z. Szűcs and B. Takács. We give examples, properties and questions of R$^*$-algebras. We observe that the class of unital commutative R$^*$-algebras has a canonical one-to-one correspondence with the class of Boolean algebras. This motivates the study of R$^*$-algebras as that of noncommutative Boolean algebras. We explain that seemingly unrelated topics of functional analysis, like AF C$^*$-algebras and incomplete inner product spaces, naturally arise in the investigation of R$^*$-algebras. We obtain a number of results on R$^*$-algebras by applying various famous theorems in the literature.
{"title":"On regular $^*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras","authors":"Michiya Mori","doi":"10.2748/tmj.20220316","DOIUrl":"https://doi.org/10.2748/tmj.20220316","url":null,"abstract":"We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of “E$^*$-algebras that are pre-C$^*$-algebras” in the sense of Z. Szűcs and B. Takács. We give examples, properties and questions of R$^*$-algebras. We observe that the class of unital commutative R$^*$-algebras has a canonical one-to-one correspondence with the class of Boolean algebras. This motivates the study of R$^*$-algebras as that of noncommutative Boolean algebras. We explain that seemingly unrelated topics of functional analysis, like AF C$^*$-algebras and incomplete inner product spaces, naturally arise in the investigation of R$^*$-algebras. We obtain a number of results on R$^*$-algebras by applying various famous theorems in the literature.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134962070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$BLO$ class under the change of measure","authors":"A. Osȩkowski","doi":"10.2748/tmj.20211208","DOIUrl":"https://doi.org/10.2748/tmj.20211208","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49215827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a class of Finsler metrics of quadratic Weyl curvature","authors":"Mehran Gabrani, E. Sevim, Z. Shen","doi":"10.2748/tmj.20220104","DOIUrl":"https://doi.org/10.2748/tmj.20220104","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42683654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction de la fonction holomorphe et bornée dans un domaine d'holomorphie de $mathbb{C}^2$","authors":"Kazuko Katô","doi":"10.2748/tmj.20210910","DOIUrl":"https://doi.org/10.2748/tmj.20210910","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42965973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Irreducibility and uniqueness of symmetric measure for Markov processes","authors":"P. He, J. Ying","doi":"10.2748/tmj.20211102","DOIUrl":"https://doi.org/10.2748/tmj.20211102","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49019670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
— Let p be a prime number, W an absolutely unramified p-adically complete discrete valuation ring with algebraically closed residue field, and X a curve over the field of fractions of W of genus greater than one. In the present paper, we study the ramification of torsion points on the curve X. A consequence of the main result of the present paper is no existence of ramified torsion point on X in the case where p is greater than three, the Jacobian variety J of X has good reduction over W , and the special fiber of the good model of J is superspecial. This consequence generalizes a theorem proved by Coleman.
{"title":"Ramification of torsion points on a curve with superspecial reduction over an absolutely unramified base","authors":"Yuichiro Hoshi","doi":"10.2748/tmj.20210604","DOIUrl":"https://doi.org/10.2748/tmj.20210604","url":null,"abstract":"— Let p be a prime number, W an absolutely unramified p-adically complete discrete valuation ring with algebraically closed residue field, and X a curve over the field of fractions of W of genus greater than one. In the present paper, we study the ramification of torsion points on the curve X. A consequence of the main result of the present paper is no existence of ramified torsion point on X in the case where p is greater than three, the Jacobian variety J of X has good reduction over W , and the special fiber of the good model of J is superspecial. This consequence generalizes a theorem proved by Coleman.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46592412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The variation of a functional on the Riemannian submanifolds and its applications","authors":"Ningwei Cui, Linfeng zhou","doi":"10.2748/tmj.20210907a","DOIUrl":"https://doi.org/10.2748/tmj.20210907a","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47629398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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