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Gaussian measure on Banach spaces

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.