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- W3197424614 abstract "For an inclusion of C*-algebras $Dsubseteq A$ with $D$ abelian, we show that when $nin A$ normalizes $D$, $n^*n$ and $nn^*$ commute with $D$. As a corollary, when $D$ is a regular MASA in $A$, every approximate unit for $D$ is also an approximate unit for $A$. This permits removal of the non-degeneracy hypothesis from the definition of a Cartan MASA in the non-unital case. We give examples of singular MASA inclusions: for some, every approximate unit for $D$ is an approximate unit for $A$, while for others, no approximate unit for $D$ is an approximate unit for $A$. If $D$ is a MASA in $A$, we ask when $A$ is a subalgebra of $B$ with $D$ a regular MASA in $B$. When $D$ is a MASA in $mathcal B(ell^2(mathbb N))$, no such $B$ exists." @default.
- W3197424614 created "2021-09-13" @default.
- W3197424614 creator A5033077197 @default.
- W3197424614 date "2021-09-02" @default.
- W3197424614 modified "2023-09-27" @default.
- W3197424614 title "Normalizers and Approximate Units for Inclusions of C*-Algebras" @default.
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