J Austral Math Soc Ser A 50 pp23--33, 1991.

The Isometries of H^p(K)

Pei-Kee Lin

Abstract

Let 1 £ p < ¥, p ¹ 2 and let K be any complex Hilbert space. We prove that every isometry T of H^p(K) onto itself is of the form

(TF)(z) = U(F °f(z)) ·(df/dz)1/p   (F Î Hp(K), |z| < 1),

where U is a unitary operator on K and f is a conformal map of the unit disc onto itself.

1980 AMS Subject Classification (1985 Revision): 46E15, 46E30

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Authors

Pei-Kee Lin

Department of Mathematics, Memphis State University, Memphis, Tennesee 38152, U.S.A.