16 problems

Let $\mathcal{A}$ be a separable, nonunital C-algebra, and let its corona be the quotient $\mathcal{Q}(\mathcal{A})=\mathcal{M}(\mathcal{A})/\mathcal{A}$ of its multiplier algebra…

Let $H$ be a separable, infinite-dimensional Hilbert space, let $\mathcal K=\mathcal K(H)$ be the algebra of compact operators, and let $\mathcal Q(H)=\mathcal B(H)/\mathcal K$ be…

Let $A$ be a separable, nonunital $\textrm{C}^*$-algebra, and let $d4c(A)$ denote its corona algebra. Let $d4cd4c$ be the Continuum Hypothesis, namely $2^{\aleph_0}=\aleph_1$. Cosk…

Let $A$ and $B$ be separable C-algebras, and let $\mathcal Q(A)$ and $\mathcal Q(B)$ denote their coronas. An isomorphism between these coronas is algebraically trivial if it arise…

Let $A$ and $D$ be separable and unital $\mathrm{C}^*$-algebras, with $D$ strongly self-absorbing. For a $\mathrm{C}^*$-algebra $B$, write $\mathcal Q(B)=\mathcal M(B)/B$ for its c…

Corona rigidity conjecture. CH implies that there are automorphisms of $\mathcal Q(A)$ that are not topologically trivial. Forcing Axioms imply that all isomorphisms between…

Let $A$ and $B$ be unital separable $\mathrm{C}^*$-algebras, let $\mathcal K$ be the algebra of compact operators on a separable Hilbert space, and let $\mathcal Q$ denote the coro…

Let $A$ and $B$ be separable $\mathrm{C}^*$-algebras, and let $\mathcal Q(A)$ and $\mathcal Q(B)$ denote their corona algebras. Algebraic isomorphism conjecture. Assume…

Let $A$ and $B$ be separable $\mathrm{C}^*$-algebras. An isomorphism between their corona algebras is algebraically trivial if it is induced by an isomorphism between suitable full…

Let $X$ and $Y$ be second countable, locally compact, noncompact spaces. Write $X^*=\beta X\setminus X$ and $Y^*=\beta Y\setminus Y$, where $\beta X$ and $\beta Y$ are their Čech–S…

Assume $\mathrm{OCA}_\infty+\mathrm{MA}_{\aleph_1}$. Let $A$ and $B$ be unital, separable $\C^*$-algebras, and let $\mathcal K(H)$ denote the compact operators on $H$. Stabilized c…

Let $A$ and $B$ be separable $\C^*$-algebras, and let a corona isomorphism be called trivial when its graph is Borel in the product of the strict topologies on the multiplier algeb…

Let $A$ be a separable, nonunital $\C^*$-algebra, and let $\mathscr{Q}(A)$ denote its corona algebra. An automorphism of $\mathscr{Q}(A)$ is trivial when its graph is Borel in the…

Let $A$ be a $[?]$

Let $\mathcal{A}$ be a separable, nonunital C-algebra, and let its corona be the quotient $\mathcal{Q}(\mathcal{A})=\mathcal{M}(\mathcal{A})/\mathcal{A}$ of its multiplier algebra…

Forcing-axiom conjecture. Forcing axioms imply that $Q(A)$ has only trivial automorphisms.