C*-supports are unique exactly when the generated C*-algebra lies in every injective envelope, yielding new characterizations of unique extension and hyperrigidity and a formula for the span of abnormalities.
The Hyperrigidity Conjecture for compact convex sets in $\mathbb{R}^2$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove that for every compact, convex subset $K\subset\mathbb{R}^2$ the operator system $A(K)$, consisting of all continuous affine functions on $K$, is hyperrigid in the C*-algebra $C(\mathrm{ex}(K))$. In particular, this result implies that the weak and strong operator topologies coincide on the set $$ \{ T\in\mathcal{B}(H);\ T\ \mathrm{normal}\ \mathrm{and}\ \sigma(T)\subset \mathrm{ex}(K) \}. $$ Our approach relies on geometric properties of $K$ and generalizes previous results by Brown.
citation-role summary
background 1
citation-polarity summary
fields
math.OA 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
$C^*$-supports and abnormalities of operator systems
C*-supports are unique exactly when the generated C*-algebra lies in every injective envelope, yielding new characterizations of unique extension and hyperrigidity and a formula for the span of abnormalities.