On combined \(H^ \infty\)-\(H^ 2\) suboptimal interpolants
type: Item
instance of: scholarly article
title: On combined \(H^ \infty\)-\(H^ 2\) suboptimal interpolants
zbMATH Open document ID: 0823.93014
DOI: 10.1016/0024-3795(94)90213-5
author: Allen Tannenbaum
author: Ciprian Foias
author: Arthur E. Frazho
published in: Linear Algebra and its Applications
publication date: 1994-08-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 614161
zbMATH Keywords: inversion
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: central commutant lifting theorem
zbMATH Keywords: \(H^ \infty\)-\(H^ 2\) suboptimality
zbMATH Keywords: suboptimal interpolants
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90213-5
OpenAlex ID: W1975777274
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description: scientific article; zbMATH DE number 614161