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In the setting of product systems over group-embeddable monoids, we consider nuclearity of the associated Toeplitz C*-algebra in relation to nuclearity of the coefficient algebra. Our work goes beyond the known cases of single…
This paper collates, presents, and expands upon technology and results obtained as part of the author's PhD thesis. We generalize work done in the $\sigma$-finite setting by the author, Goldbring, Hart, and Sinclair by producing a language…
For an extension $1\rightarrow N \rightarrow \Gamma \xrightarrow{q} \Gamma / N \rightarrow 1$ of discrete countable groups, it is known that the Baum-Connes conjecture with coefficients holds for $\Gamma$ if it holds for $\Gamma / N$ and…
We study the K-theory of the Cuntz-Nica-Pimsner C*-algebra of a rank-two product system that is an extension determined by an invariant ideal of the coefficient algebra. We use a construction of Deaconu and Fletcher that describes the…
Given an $n\times n$ random matrix $X_n$ with i.i.d. entries of unit variance, the circular law says that the empirical spectral distribution (ESD) of $X_n/\sqrt{n}$ converges to the uniform measure on the unit disk. Let $M_n$ be a…
We transfer the theory of slack operators and sums-of-squares-criteria for lifts from convex cones to operator systems. These allow to study the following question, among others: Given an abstract operator system, is its enveloping…
Using the Witten deformation and localization algebra techniques, we compute the $G$-equivariant $K$-homology class of the de Rham operator on a proper cocompact $G$-spin manifold, where $G$ is an almost connected Lie group. By applying a…
We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose a list of seven types of moves that we…
We develop important properties of the KK-functor on the basis of split exactness. In particular we discuss two slightly different short proofs for the existence of the Kasparov product and its associativity. We use the approach with…
We study the distances between the unitary orbits of matrix amplifications of elements in certain C*-algebras. In particular, we show that the distance between unitary orbits of arbitrary elements in unital, separable, UHF-stable…
The 2-adic ring $C^*$-algebra $\mathcal{Q}_2$ is the universal $C^*$-algebra generated by a unitary and an isometry satisfying certain relations. It contains a canonical copy of the Cuntz algebra $\mathcal{O}_2$. We show that…
We study sufficient conditions under which a nowhere scattered C*-algebra $A$ has a nowhere scattered multiplier algebra $\mathcal{M}(A)$, that is, we study when $\mathcal{M}(A)$ has no nonzero, elementary ideal-quotients. In particular, we…
Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective amalgam $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. In the case where $ M_1 $…
For each adjointable idempotent $Q$ on a Hilbert $C^*$-module $H$, a specific projection $m(Q)$ called the matched projection of $Q$ was introduced recently due to the characterization of the minimum value among all the distances from…
In this paper, we study $C^*$-envelopes of finite-dimensional operator algebras arising from constrained interpolation problems on the unit disc. In particular, we consider interpolation problems for the algebra $H^\infty_{\text{node}}$…
For an action of a discrete group $\Gamma$ on a set $X$, we show that the Schreier graph on $X$ has property A if and only if the permutation representation on $\ell_2X$ generates an exact $\mathrm{C}^*$-algebra. This is well known in the…
We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups and prove generalizations of Biane's theoresm. Our proof of…
There is a famous multiplication table of types of tensor product of two von Neumann algebras. We filled out the multiplication table of graded tensor product of two graded von Neumann algebras in special cases.
The aim of this paper is to give new characterizations of some fundamental issues about idempotents. In the general setting of adjointable operators on Hilbert $C^*$-modules, a new term of quasi-projection pair is introduced. For each…
This article concerns the structure of $\mathrm{C}^{\ast}$-algebraic group actions induced on corona algebras from a given $\sigma$-unital $\mathrm{C}^{\ast}$-dynamical system over a locally compact group $G$. We prove that such actions…