Does every von Neumann algebra have a matrix unit? With no assumption on a specific type In
I know that a von Neumann algebra is a direct sum of type In and II and III von Neumann algebras. I'm looking for a system of n x n(n>1) matrix unit which works in the whole algebra not in a specific direct summand of some type.
functional-analysis
asked Nov 28 '18 at 9:38
Shirin
1
add a comment |
I know that a von Neumann algebra is a direct sum of type In and II and III von Neumann algebras. I'm looking for a system of n x n(n>1) matrix unit which works in the whole algebra not in a specific direct summand of some type.
functional-analysis
asked Nov 28 '18 at 9:38
Shirin
1
I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08
add a comment |
I know that a von Neumann algebra is a direct sum of type In and II and III von Neumann algebras. I'm looking for a system of n x n(n>1) matrix unit which works in the whole algebra not in a specific direct summand of some type.
functional-analysis
asked Nov 28 '18 at 9:38
Shirin
1
I know that a von Neumann algebra is a direct sum of type In and II and III von Neumann algebras. I'm looking for a system of n x n(n>1) matrix unit which works in the whole algebra not in a specific direct summand of some type.
functional-analysis
functional-analysis
asked Nov 28 '18 at 9:38
Shirin
1
asked Nov 28 '18 at 9:38
Shirin
1
asked Nov 28 '18 at 9:38
Shirin
1
asked Nov 28 '18 at 9:38
Shirin
1
asked Nov 28 '18 at 9:38
Shirin
1
1
I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08
add a comment |
I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08
I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08
I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08
add a comment |
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I am unsure of what you mean by a matrix unit. You surely don't look for one generating the whole algebra (it would be finite-dimensional then)?
– Munk
Nov 29 '18 at 15:08