Central Intertwining Lifting, Suboptimization, and Interpolation in Several Variables

✍ Scribed by Gelu Popescu

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 196 KB
• Volume: 189
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3861

✦ Synopsis

In this paper we obtain an explicit central intertwining lifting for row contractions. This is used to prove Kaftal-Larson-Weiss and Foias ¸-Frazho H . -H 2 suboptimization type results for the noncommutative (resp. commutative) analytic Toeplitz algebra F . n (resp. W . n ). The algebra F . n (resp. W . n ) can be viewed as a multivariable noncommutative (resp. commutative) analogue of the Hardy space H . . Similar results are provided for F . n é ¯B(K, KOE) and W . n é ¯B(K, KOE), where B(K, KOE) is the set of all bounded linear operators acting on Hilbert spaces. New extensions of the Sarason, Carathéodory, and Nevanlinna-Pick type interpolation results are obtained for F . n é ¯B(K, KOE) and some consequences to the operator-valued analytic interpolation in the unit ball of C n are considered. © 2002 Elsevier Science (USA) In studying subalgebras of C g -algebras, Kaftal et al. [KLW] discovered a joint norm control Nehari type theorem. Stated for H . , their theorem says that if d > 1, f ¥ H . , and j ¥ H . is an inner function, then there exists h ¥ H . such that ||f -jh|| . [ dd . (f, jH . ) and ||f -jh|| 2 [ d `d2 -1 d 2 (f, jH . ).