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arXiv · 1507.02275

The double commutation theorem for selfdual Hilbert right W*-modules

Corneliu Constantinescu
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Abstract

Let E be a W*-algebra, H a selfdual Hilbert right E-module, L(H) the W*-algebra of adjointable operators on H, and F an involutive unital subalgebra of L(H). We prove that the double commutant of F is the W*-subalgebra of L(H) generated by F. The proofs work simultaneously for the real and for the complex case. If E is the field of real or complex numbers then H is a Hilbert space and this result becomes the well-known classical double commutation theorem.

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Corneliu Constantinescu. 2015-07-08. The double commutation theorem for selfdual Hilbert right W*-modules. https://arxiv.org/abs/1507.02275

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