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)



Minimal superalgebras of weak-$ \sp \ast$ Dirichlet algebras

Author: Takahiko Nakazi
Journal: Proc. Amer. Math. Soc. 95 (1985), 70-72
MSC: Primary 46J10
MathSciNet review: 796448
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a weak-$ * $ Dirichlet algebra in $ {L^\infty }(m)$ and let $ {H^\infty }(m)$ be the weak-$ * $ closure of $ A$ in $ {L^\infty }(m)$. It may happen that there are minimal weak-$ * $ closed subalgebras of $ {L^\infty }(m)$ that contain $ {H^\infty }(m)$ properly. In this paper it is shown that if there is a minimal, proper, weak-$ * $ closed superalgebra of $ {H^\infty }(m)$, then, in fact, that algebra is the unique least element in the lattice of all proper weak-$ * $ closed superalgebras of $ {H^\infty }(m)$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10

Retrieve articles in all journals with MSC: 46J10

Additional Information

Keywords: Minimal weak-$ * $ closed superalgebras, weak-$ * $ Dirichlet algebra, Hardy space, uniform algebra
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society