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The isometries of Hp(K)

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

Pei-Kee Lin
Pei-Kee Lin
Affiliation:
Department of Mathematics Memphis State UniversityMemphis, Tennesee 38152, U.S.A.
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Abstract

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Let 1 ≤ p < ∞, p ≠ 2 and let K be any complex Hilbert space. We prove that every isometry T of Hp(K) onto itself is of the form , where U ia a unitary operator on K and φ is a conformal map of the unit disc onto itself.

Keywords

Hardy spaceisometryHilbert spaceconformnal map

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 23 - 33
Copyright
Copyright © Australian Mathematical Society 1991

References

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