MASAS in finite von Neumann algebras

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While reading the book "Finite vN algebras and Masas", I realized the following facts.



A maximal abelian self adjoint algebra $A$ in a type $II_1$ factor $N$ is * isomorphic to $L^infty[0,1]$. But two MASAS $A_1, A_2$ in $N$ are different with respect to the size of their normalizers when one addresses the inclusion of $A_1,A_2$ in $N$.



But I am not getting any motivation for why one address the inclusion? Can one say anything about N with respect to the masas in N?(Give me a known result, if any)?



In addition what one can say about masas in $B(H)$ in terms of the normalizer of it?



Thanks in advance.




functional-analysis operator-algebras von-neumann-algebras




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    up vote
    1
    down vote

    favorite












    While reading the book "Finite vN algebras and Masas", I realized the following facts.



    A maximal abelian self adjoint algebra $A$ in a type $II_1$ factor $N$ is * isomorphic to $L^infty[0,1]$. But two MASAS $A_1, A_2$ in $N$ are different with respect to the size of their normalizers when one addresses the inclusion of $A_1,A_2$ in $N$.



    But I am not getting any motivation for why one address the inclusion? Can one say anything about N with respect to the masas in N?(Give me a known result, if any)?



    In addition what one can say about masas in $B(H)$ in terms of the normalizer of it?



    Thanks in advance.




    functional-analysis operator-algebras von-neumann-algebras




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      While reading the book "Finite vN algebras and Masas", I realized the following facts.



      A maximal abelian self adjoint algebra $A$ in a type $II_1$ factor $N$ is * isomorphic to $L^infty[0,1]$. But two MASAS $A_1, A_2$ in $N$ are different with respect to the size of their normalizers when one addresses the inclusion of $A_1,A_2$ in $N$.



      But I am not getting any motivation for why one address the inclusion? Can one say anything about N with respect to the masas in N?(Give me a known result, if any)?



      In addition what one can say about masas in $B(H)$ in terms of the normalizer of it?



      Thanks in advance.




      functional-analysis operator-algebras von-neumann-algebras




      share|cite|improve this question











      While reading the book "Finite vN algebras and Masas", I realized the following facts.



      A maximal abelian self adjoint algebra $A$ in a type $II_1$ factor $N$ is * isomorphic to $L^infty[0,1]$. But two MASAS $A_1, A_2$ in $N$ are different with respect to the size of their normalizers when one addresses the inclusion of $A_1,A_2$ in $N$.



      But I am not getting any motivation for why one address the inclusion? Can one say anything about N with respect to the masas in N?(Give me a known result, if any)?



      In addition what one can say about masas in $B(H)$ in terms of the normalizer of it?



      Thanks in advance.





      functional-analysis operator-algebras von-neumann-algebras





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 28 at 8:04









      rkmath

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