Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isometries of the disc algebra


Authors: Mohamad El-Gebeily and John Wolfe
Journal: Proc. Amer. Math. Soc. 93 (1985), 697-702
MSC: Primary 46J15; Secondary 30H05
MathSciNet review: 776205
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The linear isometries $ u:A \to A$ of the disc algebra $ A$ into itself are completely described. Such isometries $ u$ must be one of two distinct types. The first type is $ uf = \psi \cdot f(\phi )$, where $ \psi \in A$ and $ \phi \in {H^\infty }$ satisfy certain described conditions. The second type is $ uf = E(\psi \cdot f(\phi ))$, where $ \phi :Q \to T$ is any continuous function from a closed zero measure subset $ Q$ of the unit circle $ T$ onto itself, $ \psi \in C(Q)$ is unimodular, and $ E:Y \to A$ is a norm 1 extension operator, where $ Y = \left\{ {\psi \cdot f(\phi ):f \in A} \right\} \subset C(Q)$. Isometries of $ C(K)$ spaces into the disc algebra are also described.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 30H05

Retrieve articles in all journals with MSC: 46J15, 30H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776205-9
Article copyright: © Copyright 1985 American Mathematical Society