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A beginner mathmatician
A beginner mathmatician
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Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be a Jordan isomorphism if $J$ is bijective, $*$-preserving and $J(xy)=J(yx)$$J(xy+yx)=J(x)J(y)+J(y)J(x)$ for all $x,y \in \mathcal M.$

Is there any nice classification of type I von Neumann algebras up to Jordan isomorphism? Also is there is any classification of type I factors up to Jordan isomorphism?

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be a Jordan isomorphism if $J$ is bijective, $*$-preserving and $J(xy)=J(yx)$ for all $x,y \in \mathcal M.$

Is there any nice classification of type I von Neumann algebras up to Jordan isomorphism? Also is there is any classification of type I factors up to Jordan isomorphism?

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be a Jordan isomorphism if $J$ is bijective, $*$-preserving and $J(xy+yx)=J(x)J(y)+J(y)J(x)$ for all $x,y \in \mathcal M.$

Is there any nice classification of type I von Neumann algebras up to Jordan isomorphism? Also is there is any classification of type I factors up to Jordan isomorphism?

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YCor
YCor
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Jordan isomorphisc Typeisomorphisms of type I von Neumann algebras

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be Jordan isomorphisma Jordan isomorphism if $J$ is bijective  , $*$-preserving and $J(xy)=J(yx)$ for all $x,y \in \mathcal M.$ 

Is there any nice classification of Typetype I von Neumann algebras uptoup to Jordan isomorphism? Also ifis there is any classification of Typetype I factors uptoup to Jordan isomorphism?

Jordan isomorphisc Type I von Neumann algebras

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be Jordan isomorphism if $J$ is bijective  , $*$-preserving and $J(xy)=J(yx)$ for all $x,y \in \mathcal M.$ Is there any nice classification of Type I von Neumann algebras upto Jordan isomorphism? Also if there is any classification of Type I factors upto Jordan isomorphism?

Jordan isomorphisms of type I von Neumann algebras

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be a Jordan isomorphism if $J$ is bijective, $*$-preserving and $J(xy)=J(yx)$ for all $x,y \in \mathcal M.$ 

Is there any nice classification of type I von Neumann algebras up to Jordan isomorphism? Also is there is any classification of type I factors up to Jordan isomorphism?

Source Link
A beginner mathmatician
A beginner mathmatician
  • 1.9k
  • 6
  • 11

Jordan isomorphisc Type I von Neumann algebras

Let $\mathcal M$ and $\mathcal N$ be two von Neumann algebras. A linear map $J:\mathcal M\to\mathcal N$ is said to be Jordan isomorphism if $J$ is bijective , $*$-preserving and $J(xy)=J(yx)$ for all $x,y \in \mathcal M.$ Is there any nice classification of Type I von Neumann algebras upto Jordan isomorphism? Also if there is any classification of Type I factors upto Jordan isomorphism?