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edit approved Dec 15, 2013 at 11:15
Davide Giraudo
edit approved Dec 15, 2013 at 11:15
Davide Giraudo
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Given any separable Banach space B$B$ and a centered Gaussian measure Q$Q$ on it with Cameron Martin-Martin space H$H$, does there exist a Hilbert space G$G$ and a Gaussian measure W$W$ on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.

  1. $B$ is a dense subspace of $G$ and restriction of $W$ to $B$ is $Q$ (that makes $W$ supported on $B$).

  2. $(B,Q)$ and $(G,W)$ have the same Cameron-Martin space $H$.

Given any separable Banach space B and a centered Gaussian measure Q on it with Cameron Martin space H, does there exist a Hilbert space G and a Gaussian measure W on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.

Given any separable Banach space $B$ and a centered Gaussian measure $Q$ on it with Cameron-Martin space $H$, does there exist a Hilbert space $G$ and a Gaussian measure $W$ on it such that following hold

  1. $B$ is a dense subspace of $G$ and restriction of $W$ to $B$ is $Q$ (that makes $W$ supported on $B$).

  2. $(B,Q)$ and $(G,W)$ have the same Cameron-Martin space $H$.

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user44179
user44179
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Given any separable Banach space B and a centered Gaussian measure Q on it with Cameron Martin space H, does there exist a Hilbert space G and a Gaussian measure W on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.

Given any Banach space B and a centered Gaussian measure Q on it with Cameron Martin space H, does there exist a Hilbert space G and a Gaussian measure W on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.

Given any separable Banach space B and a centered Gaussian measure Q on it with Cameron Martin space H, does there exist a Hilbert space G and a Gaussian measure W on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.

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user44179
user44179
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Gaussian measure on Banach spaces

Given any Banach space B and a centered Gaussian measure Q on it with Cameron Martin space H, does there exist a Hilbert space G and a Gaussian measure W on it such that following hold

1)B is a dense subspace of G and restriction of W to B is Q(that makes W supported on B).

2)(B,Q) and (G,W) have the same cameron martin space H.