Completions of matrices and the commutant lifting theorem
Some completion results for partially defined matrices with an infinite number of entries are obtained. These are then applied to obtain a description for the dilations of intertwining operators. In this context, a new proof of the commutant lifting theorem of Sz. Nagy and Foiaş [see \textit{C. Foiaş} and \textit{A. E. Frazho}, ``The commutant lifting approach to interpolation problems'' (1990; Zbl 0718.47010)] is given. A different approach which leads to a related description of the dilations of intertwining operators was also obtained from the theory of generalized Toeplitz kernels of Arocena and Cotlar [see \textit{R. Arocena}, Integral Equations Oper. Theory 6, 759-778 (1983; Zbl 0528.47013)].
scientific article; zbMATH DE number 39683