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LSpice
LSpice
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projections Projections in a diffuse von Neumann algebra

Suppose that $M$ is a von Neumann agebraalgebra with no minimal projections. Let $p$ be a nonzero projection in $M$ and $\rho$ be a normal state on $M$.

For any $\epsilon>0$, can we find a projection $e$ in $M$ such that $0\leq e\leq p$ and $\rho(e)=\epsilon \rho(p)$?

projections in a diffuse von Neumann algebra

Suppose that $M$ is a von Neumann agebra with no minimal projections. Let $p$ be a nonzero projection in $M$ and $\rho$ be a normal state on $M$.

For any $\epsilon>0$, can we find a projection $e$ in $M$ such that $0\leq e\leq p$ and $\rho(e)=\epsilon \rho(p)$?

Projections in a diffuse von Neumann algebra

Suppose that $M$ is a von Neumann algebra with no minimal projections. Let $p$ be a nonzero projection in $M$ and $\rho$ be a normal state on $M$.

For any $\epsilon>0$, can we find a projection $e$ in $M$ such that $0\leq e\leq p$ and $\rho(e)=\epsilon \rho(p)$?

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mathbeginner
mathbeginner
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projections in a diffuse von Neumann algebra

Suppose that $M$ is a von Neumann agebra with no minimal projections. Let $p$ be a nonzero projection in $M$ and $\rho$ be a normal state on $M$.

For any $\epsilon>0$, can we find a projection $e$ in $M$ such that $0\leq e\leq p$ and $\rho(e)=\epsilon \rho(p)$?