Residually finite-dimensional operator algebras

  title={Residually finite-dimensional operator algebras},
  author={Raphael Clouatre and Christopher Ramsey},
  journal={Journal of Functional Analysis},

Finite-dimensional approximations and semigroup coactions for operator algebras

The residual finite-dimensionality of a C-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense

Finite dimensional approximations in operator algebras

. A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix

Finite Dimensionality in the Non-commutative Choquet Boundary: Peaking Phenomena and C*-Liminality

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

Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and $\mathrm{C}^*$-liminality.

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

Multiplier tests and subhomogeneity of multiplier algebras

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel

Some notes on the universal C*-algebra of a contraction

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal

Maximal C⁎-covers and residual finite-dimensionality

  • I. Thompson
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2022

Identification of maximal $C^*$-covers of some operator algebras

In 1999, Blecher [2] introduced the concept of the maximal C-cover of an operator algebra. This algebra encodes the completely contractive representation theory of an operator algebra. In particular,

Quasitriangular operator algebras

. We give characterizations of quasitriangular operator algebras along the line of Voiculescu’s characterization of quasidiagonal C ∗ -algebras. their representations. Note that in the selfadjoint



Residual finite dimensionality and representations of amenable operator algebras

Operator Spaces and Residually Finite-Dimensional C*-Algebras

Abstract For every operator space X the C *-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In

Modules over Operator Algebras, and the Maximal C*-Dilation☆☆☆

Abstract We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to


Crossed Products of Operator Algebras

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the

Elements of $C^{\ast }$ -algebras Attaining their Norm in a Finite-dimensional Representation

Abstract We characterize the class of RFD $C^{\ast }$ -algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that

Noncommutative semialgebraic sets and associated lifting problems

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a

On residually finite-dimensional *-algebras

Exel and Loring have listed several conditions that are equivalent to the residual finite-dimensionality of a C*-algebra. We review and extend this list. A C*-algebra is said to be residually


In analogy with the peak points of the Shilov boundary of a uni- form algebra, Arveson defined the notion of boundary representations among the completely contractive representations of a unital