Related papers: The Hyperrigidity Conjecture for Spectrahedra

The following generalization of a result of S. Nemirovski is proved: if $X$ is either a projective or a Stein manifold and $K\subset X$ is a compact sublevel set of a strictly plurisubharmonic function $\varphi$ defined in a neighborhood of…

We present a general setting to investigate U_fin-cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this setting we give new proofs to some U_fin-cocycle superrigidity results of S. Popa…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

Let $G$ be a Lie group with real semisimple Lie algebra $\mathfrak{g}$. Further let $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}$ be a Cartan decomposition. The maximal compact subgroup $K \subseteq G$ acts on $\mathfrak{p}$ via the…

We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the…

We show that the reduced groupoid C*-algebras of continuous fields of \'etale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable…

We introduce a wide subclass ${\cal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact K\"ahler manifold, on which the complex Monge-Amp\`ere operator is well-defined and the convergence theorem is valid. We also prove that…

Let $\Phi$ be a family of functions analytic in some neighborhood of a complex domain $\Omega$, and let $T$ be a Hilbert space operator whose spectrum is contained in $\overline\Omega$. Our typical result shows that under some extra…

For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\operatorname{Fix} B$, of any family $B$ of endomorphisms of $\pi_1(\Sigma)$ is compressed in $\pi_1(\Sigma)$ i.e.,…

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

For a $C^*$-algebra $A$ of compact operators and a compact manifold $M,$ we prove that the Hodge theory holds for $A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective $A$-Hilbert…

We investigate the hyperrigidity of subsets of unital $C^*$-algebras annihilated by states (or, more generally, by completely positive maps). This is closely related to the concept of rigidity at $0$ introduced by G. Salomon, who studied…

In this article, we show that, if $S\in \mathcal{B}(H)$ is irreducible and essential unitary, then $\{S,SS^*\}$ is a hyperrigid generator for the unital $C^*$-algebra $\mathcal{T}$ generated by $\{S,SS^*\}$. We prove that, if $T$ is an…

We find necessary and sufficient conditions for the subalgebra of analytic elements associated with a periodic C*-dynamical system to be a maximal norm-closed subalgebra. Our conditions are in terms of the Arveson spectrum of the action. We…

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…

We show that, if a simple $C^{*}$-algebra $A$ is topologically finite-dimensional in a suitable sense, then not only $K_{0}(A)$ has certain good properties, but $A$ is even accessible to Elliott's classification program. More precisely, we…

Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely…

We show that the Kazhdan-Lusztig category $KL_k$ of level-$k$ finite-length modules with highest-weight composition factors for the affine Lie superalgebra $\widehat{\mathfrak{gl}(1|1)}$ has vertex algebraic braided tensor supercategory…

We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.

We consider a class of dynamical systems with compact non abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point…