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

2015/07/08 by Corneliu Constantinescu, Constantinescu, Corneliu
Mathematics · #46L08 (Primary) #46L10 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L08 #msc:46L10

paper · pdf · doi:10.48550/arxiv.1507.02275

8 pages

arxiv created 2015/07/08 · arxiv updated 2015/07/10

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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