×

A maximum problem for operators. (English) Zbl 0547.47004

The article under review is a survey devoted to the following extremum problem. Let p be a polynomial, H be an n-dimensional Hilbert space. The problem is to maximize \(\| T^ n\|\) (or more generally to maximize \(\|\phi (T)\|\) for a given polynomial \(\phi)\), T being a contraction on H annihilated by p. Connections with the Sz.-Nagy- Foiaş model and Hankel and Toeplitz operators are considered.
Reviewer: V.V.Peller

MSC:

47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47A60 Functional calculus for linear operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A45 Canonical models for contractions and nonselfadjoint linear operators