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Corrected typo.
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Bill Johnson
Bill Johnson
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Q1 is equivalent to the separable quotient problem. Indeed, given $Y$$X$ infinite dimensional, let $W$ be any separable infinite dimensional subspace of $X^*$ and let $Y$ be the annihilator of $W$ in $X$. Then the dual of $X/Y$ is the weak$^*$ closure of $W$ in $X^*$.

Q1 is equivalent to the separable quotient problem. Indeed, given $Y$ infinite dimensional, let $W$ be any separable infinite dimensional subspace of $X^*$ and let $Y$ be the annihilator of $W$ in $X$. Then the dual of $X/Y$ is the weak$^*$ closure of $W$ in $X^*$.

Q1 is equivalent to the separable quotient problem. Indeed, given $X$ infinite dimensional, let $W$ be any separable infinite dimensional subspace of $X^*$ and let $Y$ be the annihilator of $W$ in $X$. Then the dual of $X/Y$ is the weak$^*$ closure of $W$ in $X^*$.

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Bill Johnson
Bill Johnson
  • 31.5k
  • 5
  • 90
  • 138

Q1 is equivalent to the separable quotient problem. Indeed, given $Y$ infinite dimensional, let $W$ be any separable infinite dimensional subspace of $X^*$ and let $Y$ be the annihilator of $W$ in $X$. Then the dual of $X/Y$ is the weak$^*$ closure of $W$ in $X^*$.