Based on the solution of \textbf{ Paulsen Problem} by Kwok, Lau, Lee, and Ramachandran [\textit{ STOC'18-Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018}] and independently by Hamilton, and Moitra [\textit{ Isr. J. Math., 2021}] we study Paulsen Problem and Projection Problem in the context of Hilbert C*-modules. We show that for commutative C*-algebras, if Modular Paulsen Problem has a solution, then Modular Projection Problem also has a solution. We formulate the problem of operator scaling for matrices over C*-algebras.
Categories: math.FA math.DS