Abstract
We study how positive completion problems over matrices with complex entries generalize to the setting of matrices with C*-algebra entries. In particular, it is observed that some C*-algebras have the Toeplitz banded completion property but fail to have the completion property for the complete graph with one undirected edge missing. Positive completions in the framework of multi-level Toeplitz matrices are also studied. Many open problems are formulated.
Mathematics Subject Classification. 46L05 (47A57).
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Dedicated to J.W. Helton on the occasion of his 65th birthday
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Rodman, L., Woerdeman, H.J. (2012). Positive Completion Problems Over C*-algebras. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_20
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DOI: https://doi.org/10.1007/978-3-0348-0411-0_20
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