Norms of composition operators with rational symbol. (English) Zbl 1107.47018

Among the analytic selfmaps \(\phi\) on the unit disc which are non-inner rational functions in \({\mathbb C^*}\), the authors find a collection where the norm of the composition operator \(\| C_\phi\| \) on the Hardy space \(H^2\) can be computed from a given quadratic expression. They compare their results with those proved by C. Hammond [Acta Sci. Math. 69, No. 3–4, 813–829 (2003; Zbl 1071.47508)] in the case of linear fractional maps and the one by C. C. Cowen [Integral Equations Oper. Theory 11, No. 2, 151–160 (1988; Zbl 0638.47027)] for linear maps.


47B33 Linear composition operators
47B38 Linear operators on function spaces (general)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
Full Text: DOI


[1] Bourdon, P.S.; Fry, E.E.; Hammond, C.; Spofford, C.H., Norms of linear-fractional composition operators, Trans. amer. math. soc., 356, 2459-2480, (2004) · Zbl 1038.47500
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[5] Hammond, C., On the norm of a composition operator with linear fractional symbol, Acta sci. math. (Szeged), 69, 813-829, (2003) · Zbl 1071.47508
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