On combined \(H^ \infty\)-\(H^ 2\) suboptimal interpolants
First, we discuss the inversion of skew Toeplitz operators. Then, we deduce the Kaftal-Larson-Weiss theorem [\textit{V. Kaftal}, \textit{D. Larson} and \textit{G. Weiss}, ``Quasitriangular subalgebras of semifinite von Neumann algebras are closed'', J. Funct. Anal. (to appear)] from the central commutant lifting theorem. This argument will highlight the role of the central or maximum entropy commuting lifting in this topic. We also define our notion of ``combined \(H^ \infty\)-\(H^ 2\) suboptimality''. We further describe a method for writing down combined \(H^ \infty\)-\(H^ 2\) interpolants, based on our parametrization of all suboptimal interpolants from [the first and third author, ``On the parametrization of the suboptimal solutions in generalized interpolation, Linear Algebra Appl. 122/123/124, 145-164 (1989; Zbl 0682.93018)]. Finally, using techniques from the first two authors, ``The commutant lifting approach to interpolation problems'', Birkhäuser, Basel (1990; Zbl 0718.47010)], we give an alternative way of finding the mixed \(H^ \infty\)-\(H^ 2\) suboptimal interpolants.
scientific article; zbMATH DE number 614161