Pták, Vlastimil A maximum problem for operators. (English) Zbl 0547.47004 Čas. Pěst. Mat. 109, 168-193 (1984). 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 Cited in 4 Documents 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 Keywords:extremum problem; contraction; Sz.-Nagy-Foiaş model; Hankel and Toeplitz operators × Cite Format Result Cite Review PDF Full Text: DOI EuDML