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Structure For Regular Inclusions. Ii Cartan Envelopes, Pseudo-Expectations And Twists, David R. Pitts
Structure For Regular Inclusions. Ii Cartan Envelopes, Pseudo-Expectations And Twists, David R. Pitts
Department of Mathematics: Faculty Publications
We introduce the notion of a Cartan envelope for a regular inclusion (C,Ɗ). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,Ɗ) regularly embeds. We prove a Cartan envelope exists if and only if (C,Ɗ) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property.
For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,Ɗ) in terms of a twist …
Structure For Regular Inclusions. I, David R. Pitts
Structure For Regular Inclusions. I, David R. Pitts
Department of Mathematics: Faculty Publications
We give general structure theory for pairs (C,D) of unital C*- algebras where D is a regular and abelian C*-subalgebra of C.
When D is maximal abelian in C, we prove existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D such that EjD = idD; E is a useful replacement for a conditional expectation when no expectation exists. When E is faithful, (C,D) has numerous desirable properties: e.g. the linear span of the normalizers has a unique minimal C*- norm; D norms C; and isometric isomorphisms of norm-closed subalgebras lying …