Abstract
We formulate and prove the commutant lifting theorem for contractions on Kreĭn spaces in the language of categories of modules. Our method is inspired by a proof of the commutant lifting theorem on Hilbert spaces due to Arocena, and provides a possible framework for other versions of the commutant lifting theorem. Additionally, the projective modules in our category are described, and it is shown that certain indices related to the adjoint of the intertwining operator are preserved during lifting.
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Dritschel, M.A. (2001). A Module Approach to Commutant Lifting on Kreĭn Spaces. In: Alpay, D., Vinnikov, V. (eds) Operator Theory, System Theory and Related Topics. Operator Theory: Advances and Applications, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8247-7_9
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DOI: https://doi.org/10.1007/978-3-0348-8247-7_9
Publisher Name: Birkhäuser, Basel
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