Related papers: Some functorial properties of Schatten classes

We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.

We study quasidiagonality and local reflexivity for $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. We introduce and study a notion of amenability for vector valued traces.

We develop a representation theory for $\lambda$-lattices, arising as standard invariants of subfactors, and for rigid C*-tensor categories, including a definition of their universal C*-algebra. We use this to give a systematic account of…

We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.

We introduce a category of inverse semigroup actions and a category of \'etale groupoids. We show that there are three functors which send inverse semigroups to their spectral actions, inverse semigroup actions to their transformation…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

RO*-algebras are defined and studied. For RO*-algebra T, using properties of partial order, it is established that the set of bounded elements can be endowed with C*-norm. The structure of commutative subalgebras of T is considered and the…

The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\Omega$ of objects belonging…

A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…

In this work, I develop a new view of presentation theory for C*-algebras, both unital and non-unital, heavily grounded in classical notions from algebra. In particular, I introduce Tietze transformations for these presentations, which lead…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

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…

We prove that ideals in amenable second-countable non-Hausdorff \'etale groupoid $C^*$-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the…

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 introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of…

We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in \'etale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

Via Gelfand duality, a unital C*-algebra $A$ induces a functor from compact Hausdorff spaces to sets, $\mathsf{CHaus}\to\mathsf{Set}$. We show how this functor encodes standard functional calculus in $A$ as well as its multivariate…