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1. Support expansion C*-algebras

   Braga, B M; Eisner, J; Sherman, D (October 2025, Journal of operator theory)

   We consider operators on L_2 spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are C*-algebras that arise from suitable families of constraints, which we call support expansion C*-algebras. In the discrete setting, support expansion C*-algebras are classical uniform Roe algebras, and the continuous version featured here provides examples of “measurable" or “quantum" uniform Roe algebras as developed in a companion paper. We find that in contrast to the discrete setting, the poset of support expansion C*-algebras inside B(L_2(R)) is extremely rich, with uncountable ascending chains, descending chains, and antichains. 

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2. C∗-algebras isomorphically representable onlp

   https://doi.org/10.2140/apde.2020.13.2173  

   Boedihardjo, March T. (January 2020, Analysis & PDE)

   null (Ed.)
3. Complexity rank for C*-algebras

   Jaime, Arturo; Willett, Rufus (January 2023, Münster journal of mathematics)

   Cuntz, Joachim (Ed.)

   Complexity rank for C*-algebras was introduced by the second author and Yu for applications towards the UCT: very roughly, this rank is at most n if you can repeatedly cut the C∗-algebra in half at most n times, and end up with something finite-dimensional. In this paper, we study complexity rank, and also a weak complexity rank that we introduce; having weak complexity rank at most one can be thought of as “two-colored local finite-dimensionality”. We first show that, for separable, unital, and simple C*-algebras, weak complexity rank one is equivalent to the conjunction of nuclear dimension one and real rank zero. In particular, this shows that the UCT for all nuclear C*-algebras is equivalent to equality of the weak complexity rank and the complexity ranks for Kirchberg algebras with zero K-theory groups. However, we also show using a K-theoretic obstruction (torsion in K1) that weak complexity rank one and complexity rank one are not the same in general. We then use the Kirchberg–Phillips classification theorem to compute the complexity rank of all UCT Kirchberg algebras: it equals one when the K1-group is torsion-free, and equals two otherwise. 

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4. Multivariable pseudospectrum in C⁎-algebras

   https://doi.org/10.1016/j.jmaa.2025.129241  

   Cerjan, Alexander; Lauric, Vasile; Loring, Terry A (July 2025, Journal of Mathematical Analysis and Applications)
5. Coupling capacity in C*-algebras

   https://doi.org/10.1017/prm.2023.81  

   Skalski, Adam; Todorov, Ivan G; Turowska, Lyudmila (February 2025, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)

   Given two unital C*-algebras equipped with states and a positive operator in the enveloping von Neumann algebra of their minimal tensor product, we define three parameters that measure the capacity of the operator to align with a coupling of the two given states. Further, we establish a duality formula that shows the equality of two of the parameters for operators in the minimal tensor product of the relevant C*-algebras. In the context of abelian C*-algebras, our parameters are related to quantitative versions of Arveson's null set theorem and to dualities considered in the theory of optimal transport. On the other hand, restricting to matrix algebras we recover and generalize quantum versions of Strassen's theorem. We show that in the latter case our parameters can detect maximal entanglement and separability. 

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