Related papers: Large irredundant sets in operator algebras
Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…
In present work we deal with the class $\mathcal{C}=\mathcal{C}_1\cup \mathcal{C}_2$ where $\mathcal{C}_1$ (respectively, $\mathcal{C}_2$) is formed by all separable Uniform algebras (respectively, separable commutative C$^*$-algebras) with…
It is well-known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing…
We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a…
We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional $\mathrm{C}^*$-algebras, in the…
We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…
We prove that Voiculescu's noncommutative version of the Weyl-von Neumann theorem can be extended to all (not necessarily separable) unital, separably representable C*-algebras whose density character is strictly smaller than…
Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on…
We investigate the representation theory of the crossed-product C*-algebra associated to a compact group G acting on a locally compact space X when the stability subgroups vary discontinuously. Our main result applies when G has a principal…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
We show that a topologically generating set $S$ of a connected compact Lie group $G$ of size larger than a fixed polynomial in the rank of $G$ must be redundant (i.e., some proper subset of $S$ still topologically generates $G$). Similar…
A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…
The radius of comparison is an invariant for unital C*-algebras which extends the theory of covering dimension to noncommutative spaces. We extend its definition to general C*-algebras, and give an algebraic (as opposed to…
We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric representations whose generating C*-algebra is not RFD.…
We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…
Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if (W*(x)' cap M) unitally contains a factor of type I_n. We decide the density of the n-divisible operators, for various n,…
In the field of constraint satisfaction problems (CSP), a clause is called redundant if its satisfaction is implied by satisfying all other clauses. An instance of CSP$(P)$ is called non-redundant if it does not contain any redundant…
For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…
Let M be a tracial von Neumann algebra and A be a weakly dense unital C*-subalgebra of M. We say that a set X is a W*-generating set for M if the von Neumann algebra generated by X is M and that X is a C*-generating set for A if the unital…
We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C*-algebras which agree on K-theory and traces. The algebras do not absorb the Jiang-Su algebra Z tensorially, answering a question of N. C.…