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math.OA2025
Kaplansky's problem and unitary orbits in matrix amplifications
Laurent W. Marcoux, Pawel Sarkowicz, Yuanhang Zhang
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 ar…
math.OA2023
Unitary groups, K-theory and traces
Pawel Sarkowicz
We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplice…
math.OA2023
Polar decomposition in algebraic K-theory
Pawel Sarkowicz, Aaron Tikuisis
We show that the Hausdorffized algebraic K-theory of a C*-algebra decomposes naturally as a direct sum of the Hausdorffized unitary algebraic K-theory and the space of continuous a…