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Consequently the weak closure of any masa bimodule of trace class operators is strongly reflexive.
We describe the weak closure of the image of the Weil representation of the infinite-dimensional symplectic group over a non-Archimedean field of an odd residue characteristic.
Let be the weak closure of.
Note that (the weak closure of ) is a weakly closed subset of for each.
For the reader's convenience we recall here the definition of the weak closure.
Here is a multivalued operator and denotes the weak closure of the set.
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We denote by and, the set of positive integers and the closure (weak closure) of a set in, respectively.
We denote by ℕ and cl(M) (wcl(M)), the set of positive integers and the closure (weak closure) of a set M in X, respectively.
Then by Mazur's theorem this set coincides with the sequential weak closure of Λ in (L^{p}(Omega )), that is, (overline{Lambda}=operatorname{cl}_{wL^{p}(Omega)} Lambda).
We denote and (resp., ) by the set of positive integers and the closure (resp., weak closure) of a set in, respectively.
If W ⊆ X ∗, then clW denotes the weak∗ closure of W. For the whole paper, we endow X ∗ × R with the product topology of w ∗ ( X ∗, X ) and the usual Euclidean topology.
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