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We introduce the Property (C) for a unital commutative sub-C*-algebra $D$ of a unital C*-algebra $A$, a version of the relative comparison property using almost normalizers. Under the assumption of this property, the $\mathcal Z$-absorption…

We analyze semigroups of decomposable maps on C*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including $B(\mathcal{H})$ for $\mathcal{H}$ a Hilbert space, is also…

Quantum metric Choquet simplices are special kinds of compact quantum metric spaces designed for distance measurement in and around the category of stably finite Elliott-classifiable $\mathrm{C}^*$-algebras. The primary objective of this…

Let $\mathcal{A}$ be a separable nuclear C*-algebra, and let $\mathcal{M}$ be a semifinite von Neumann factor with separable predual. Let $\phi, \psi: \mathcal{A} \rightarrow \mathcal{M}$ be essential trivial extensions with $\phi(a) -…

We present a new method, involving monads and comonads from category theory, to help establish a certain type of equivalence of subcategories. As a case study we consider the category of topological gradings of $C^*$-algebras over a fixed…

We give conditions when not necessarily adjointable operators between Hilbert modules allow for a polar decomposition involving not necessarily adjointable partial isometries. While the latter have been introduced and discussed by Shalit…

We describe proper actors from the underlying groupoid of a graph C*-algebra to another \'etale groupoid in terms of bisections. This allows to understand graph morphisms and the *-homomorphisms that they induce more conceptually. More…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant…

We characterize covariant positive decomposable maps between unital C*-algebras in terms of a dilation theorem, which generalizes a seminal result by H. Scutaru from Rep. Math. Phys. 16 (1):79-87, 1979. As a case study, we provide a certain…

The authors' recent classification of Jesper Villadsen's remarkable generalization (based on a self-reproducing seed space) of Glimm's infinite tensor product (UHF) C*-algebras, by means of the Cuntz semigroup (in the case of a fixed,…

In this paper, we will prove alternate conditions for a type-$III$ Bernoulli scheme to be of type-$III_0$, type-$III_{\lambda}$ and type-$III_1$, and then conclude an alternate definition of the asymptotic ratio set of a type-$III$ ITPFI…

We define $\Delta$-equivalence for dual operator systems and prove that it is an equivalence relation. We show that weak TRO-equivalence of dual operator spaces induces a stable isomorphism between them which is given by multiplication with…

We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital, C*-algebras endowed with an analogue of the Lipschitz…

Let $\mathcal{M}$ be a separable von Neumann algebra with center $\mathcal{Z}(\mathcal{M})$. An operator $T$ in $\mathcal{M}$ is called irreducible if the von Neumann algebra $W^*(T)$ generated by $T$ has trivial relative commutant, i.e.,…

We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular implies that all intermediate C*-algebras are selfless in the sense of Robert. We identify natural sources of selfless…

Suppose $\mathscr M$ and $\mathscr N$ are von Neumann algebras. Two operators $A$ and $B$ in $\mathscr M$ are said to be orthogonal if $A^*B=0$, meaning their ranges are orthogonal. Let $\varphi\colon\mathscr M\to\mathscr N$ be a map. We…

Let $\big((A^{(i)}, G, \alpha^{(i)}), \phi_i\big)_{i \in \mathbb{N}}$ be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action $\alpha$ of $G$ on the inductive limit $A=\varinjlim A^{(i)}$.…

In this article, we explore the quantum symmetry of the direct sum of a finite family of Cuntz algebras $\{\mathcal{O}_{n_i} \}_{i=1}^{m}$, viewing them as graph $C^*$-algebras associated to the graphs $\{L_{n_i}\}_{i=1}^{m}$ (where $L_n$…

We construct a family of operator systems and $k$-AOU spaces generated by a finite number of projections satisfying a set of linear relations. This family is universal in the sense that the map sending the generating projections to any…