• Corpus ID: 117246221


  author={David R. Pitts},
  journal={arXiv: Operator Algebras},
  • D. Pitts
  • Published 28 February 2012
  • Mathematics
  • arXiv: Operator Algebras
We study pairs (C,D) of unital C*-algebras where D is a regular abelian C*-subalgebra of C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D whose restriction to D is the identity on D. We show that the left kernel of E, L(C,D), is the unique closed two-sided ideal of C maximal with respect to having trivial intersection with D. When L(C,D)=0, we show the MASA D norms C. We apply these results to extend… 
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