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)

 

 

Bounded sections on a Riemann surface


Author: Walter Pranger
Journal: Proc. Amer. Math. Soc. 69 (1978), 77-80
MSC: Primary 46J15; Secondary 30A98
DOI: https://doi.org/10.1090/S0002-9939-1978-0482224-9
MathSciNet review: 0482224
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X denote a hyperbolic Riemann surface, $ \zeta $ a unitary line bundle, and $ {H^\infty }(\zeta )$ the Banach space of bounded holomorphic sections of $ \zeta $. If, for a given point $ \xi $ in X, the norm of the evaluation functional on $ {H^\infty }(\zeta )$ varies continuously with the bundle $ \zeta $, then it is shown that the space of bounded holomorphic sections is dense in the space of holomorphic sections for every unitary line bundle.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 30A98

Retrieve articles in all journals with MSC: 46J15, 30A98


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0482224-9
Article copyright: © Copyright 1978 American Mathematical Society