An intersection result for tensor products of 𝐶*-algebras

Abstract

We consider A and B canonically embedded in their enveloping W*algebras A** and B**, so that A ® B is contained in v4** ® B** canonically. Let C " and D ~ be the weak closures of C and D. Theorem. With the above situation, if F(C, D) strictly contains C ® D and there exist projections of norm one from A** and B** onto C~ and D~, respectively, then (A <S) B) n (C~ ® D ~) strictly contains (A n C") ® (B n D-).

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