Related papers: Finite dimensional approximations in operator alge…

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.…

The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…

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…

The C*-envelope of a non self-adjoint operator algebra is known to encode many properties of the underlying subalgebra. However, the C*-envelope does not always encode the residual finite-dimensionality of an operator algebra. To elucidate…

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…

For every operator space $X$ the $C^\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free $C^\ast$-algebra on any…

It is proved that the C*-algebra of a graph is residually finite dimensional (RFD) if and only if the graph has no infinite receiver, no cycle with an exit, no infinite ackward chain and from each vertex, there is a finite path to a sink or…

We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…

The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…

We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such representations may fail to exist even when the underlying…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

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 weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor…

An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…

Let $k$ be an algebraically closed field of characteristic 0, $Y=k^{r}\times {(k^{\times})}^{s}$ and let $G$ be an algebraic torus acting diagonally on the ring of differential operators $\cD (Y)^G$. We give necessary and sufficient…

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated…

An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the…

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…

A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions,…