Abstract
We study the maximal abelian von Neumann algebra corresponding to L ∞ ( R ) L^\infty (\mathbb {R}) via the Bargmann transform. It is naturally an algebra of operators on the Fock space F 2 F^2 , but it can also be realized as a function algebra contained in F 2 F^2 . This provides an interesting example of a C ∗ C^* algebra whose elements are analytic functions.
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