Related papers: Separability idempotents in C*-algebras

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…

The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the…

In this paper, we introduce quotients of \'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an \'etale groupoid…

We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

Characterisations of those separable C*-algebras that have type I injective envelopes or W*-algebra injective envelopes are presented.

We develop a general framework to deal with the unitary representations of quantum groups using the language of C*-algebras. Using this framework, we prove that the duality holds in a general context. This extends the framework of the…

We study the link between stably finiteness and stably projectionless-ness for $C^*$-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by $4$; otherwise, they…

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms…

We characterize the topology of the Glimm space of a separable C*-algebra and extend the main result of [6] to non-unital AF C*-algebras.

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…

It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C*-algebra to agree with the first.

In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…

We define a basis property that an inclusion of C*-algebras $\mathcal O_\infty\subset A$ may have, and give various conditions for the property to hold. Some applications are considered. We also give a characterization of open projections…

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.