Norms of composition operators on the Hardy space. (English) Zbl 0862.47015

Summary: We show that the norm of a composition operator on the classical Hardy space \(H^2\) cannot be computed using only the set of \(H^2\) reproducing kernels, answering a question raised by Cowen and MacCluer.


47B38 Linear operators on function spaces (general)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
Full Text: DOI Euclid EuDML EMIS


[1] Cowen C. C., Integral Equations and Operator Theory 11 pp 151– (1988) · Zbl 0638.47027
[2] Cowen C. C., Composition Operators on Spaces of Analytic Functions (1995) · Zbl 0873.47017
[3] Duren P. L., Theory of H spaces (1970) · Zbl 0215.20203
[4] Littlewood J. E., Proc. London Math. Soc.(2) 23 pp 481– (1925)
[5] Nordgren E. A., Canadian J. Math. 20 pp 442– (1968) · Zbl 0161.34703
[6] Ryf J. V., Duke Math. J. 33 pp 347– (1966) · Zbl 0148.30205
[7] Shapiro J. H., Ann. Math. 125 pp 375– (1987) · Zbl 0642.47027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.