construct an element in $prod M_{k(n)} (mathbb{C})$
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Suppose $A$ is a $C^*$ algebra,$oplus_{c_0} M_{k(n)} (mathbb{C} )$ is a essential ideal of $A$ and there is an element $(x_n) in A$ such that $(x_n) in prod M_{k(n)} (mathbb{C})$ and $tr(x_n) to 0,$ where $x_n in M_{k(n)}(mathbb{C}),tr()$ is the tracial state on $M_{k(n)} (mathbb{C})$.
Can we construct an element $(y_n) in A$ through $(x_n)$ such that $(y_n) in prod M_{k(n)} (mathbb{C})$ and $tr(y_n)$ does not converge to 0.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Nov 16 at 16:08
mathrookie
697512
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Suppose $A$ is a $C^*$ algebra,$oplus_{c_0} M_{k(n)} (mathbb{C} )$ is a essential ideal of $A$ and there is an element $(x_n) in A$ such that $(x_n) in prod M_{k(n)} (mathbb{C})$ and $tr(x_n) to 0,$ where $x_n in M_{k(n)}(mathbb{C}),tr()$ is the tracial state on $M_{k(n)} (mathbb{C})$.
Can we construct an element $(y_n) in A$ through $(x_n)$ such that $(y_n) in prod M_{k(n)} (mathbb{C})$ and $tr(y_n)$ does not converge to 0.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Nov 16 at 16:08
mathrookie
697512
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose $A$ is a $C^*$ algebra,$oplus_{c_0} M_{k(n)} (mathbb{C} )$ is a essential ideal of $A$ and there is an element $(x_n) in A$ such that $(x_n) in prod M_{k(n)} (mathbb{C})$ and $tr(x_n) to 0,$ where $x_n in M_{k(n)}(mathbb{C}),tr()$ is the tracial state on $M_{k(n)} (mathbb{C})$.
Can we construct an element $(y_n) in A$ through $(x_n)$ such that $(y_n) in prod M_{k(n)} (mathbb{C})$ and $tr(y_n)$ does not converge to 0.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Nov 16 at 16:08
mathrookie
697512
Suppose $A$ is a $C^*$ algebra,$oplus_{c_0} M_{k(n)} (mathbb{C} )$ is a essential ideal of $A$ and there is an element $(x_n) in A$ such that $(x_n) in prod M_{k(n)} (mathbb{C})$ and $tr(x_n) to 0,$ where $x_n in M_{k(n)}(mathbb{C}),tr()$ is the tracial state on $M_{k(n)} (mathbb{C})$.
Can we construct an element $(y_n) in A$ through $(x_n)$ such that $(y_n) in prod M_{k(n)} (mathbb{C})$ and $tr(y_n)$ does not converge to 0.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Nov 16 at 16:08
mathrookie
697512
asked Nov 16 at 16:08
mathrookie
697512
asked Nov 16 at 16:08
mathrookie
697512
asked Nov 16 at 16:08
mathrookie
697512
asked Nov 16 at 16:08
mathrookie
697512
697512
add a comment |
add a comment |
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