Minimal or Maximal Von Neumann algebra contained in a given $C^*$ algebra
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Let $A,B subset B(H)$ be two concrete von Neumann algebra. Is $Acap B$ a von Neumann algebra, too?
What about the intrinsic analogy of this question, as follows:
Let $C$ be a $C^*$ algebra and $A,B subset C$ be two von Neumann algebras. Is their intersection, a von Neumann algebra, too?
Can one speak of a kind of minimal von Neumann algebra contained in a given $C^*$ algebra?
On the other extreme, can one think of a kind of maximal von Neumann algebra contained in a given $C^*$ algebra?
In particular what are two maximal von neumann algebras in $B(H)$ which are not isomorphic?
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked 11 hours ago
Ali Taghavi
199329
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up vote
1
down vote
favorite
Let $A,B subset B(H)$ be two concrete von Neumann algebra. Is $Acap B$ a von Neumann algebra, too?
What about the intrinsic analogy of this question, as follows:
Let $C$ be a $C^*$ algebra and $A,B subset C$ be two von Neumann algebras. Is their intersection, a von Neumann algebra, too?
Can one speak of a kind of minimal von Neumann algebra contained in a given $C^*$ algebra?
On the other extreme, can one think of a kind of maximal von Neumann algebra contained in a given $C^*$ algebra?
In particular what are two maximal von neumann algebras in $B(H)$ which are not isomorphic?
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked 11 hours ago
Ali Taghavi
199329
1
For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $A,B subset B(H)$ be two concrete von Neumann algebra. Is $Acap B$ a von Neumann algebra, too?
What about the intrinsic analogy of this question, as follows:
Let $C$ be a $C^*$ algebra and $A,B subset C$ be two von Neumann algebras. Is their intersection, a von Neumann algebra, too?
Can one speak of a kind of minimal von Neumann algebra contained in a given $C^*$ algebra?
On the other extreme, can one think of a kind of maximal von Neumann algebra contained in a given $C^*$ algebra?
In particular what are two maximal von neumann algebras in $B(H)$ which are not isomorphic?
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked 11 hours ago
Ali Taghavi
199329
Let $A,B subset B(H)$ be two concrete von Neumann algebra. Is $Acap B$ a von Neumann algebra, too?
What about the intrinsic analogy of this question, as follows:
Let $C$ be a $C^*$ algebra and $A,B subset C$ be two von Neumann algebras. Is their intersection, a von Neumann algebra, too?
Can one speak of a kind of minimal von Neumann algebra contained in a given $C^*$ algebra?
On the other extreme, can one think of a kind of maximal von Neumann algebra contained in a given $C^*$ algebra?
In particular what are two maximal von neumann algebras in $B(H)$ which are not isomorphic?
operator-theory operator-algebras c-star-algebras von-neumann-algebras
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked 11 hours ago
Ali Taghavi
199329
asked 11 hours ago
Ali Taghavi
199329
edited 4 hours ago
asked 11 hours ago
Ali Taghavi
199329
asked 11 hours ago
Ali Taghavi
199329
asked 11 hours ago
Ali Taghavi
199329
199329
1
For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago
add a comment |
1
For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago
1
1
For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago
For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago
add a comment |
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For the first question the answer is yes, because intersection behaves nicely in both algebra and topology. For the rest, I prefer $C^*$-algebras over von-Neumann algebras, so wait for an expert to reply.
– Aweygan
10 hours ago