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Topology of the Maximal Ideal Space of H∞

✍ Scribed by Alexander Brudnyi


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
252 KB
Volume
189
Category
Article
ISSN
0022-1236

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✦ Synopsis


We give a topological description of the maximal ideal space M(H . ) of the algebra H . =H . (D) of bounded analytic functions defined on the open unit disk D … C. Our results are based on a construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spaces of compact manifolds.


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Uniformity of the Meager Ideal and Maxim
✍ Jörg Brendle; Otmar Spinas; Yi Zhang 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 142 KB

We prove that every maximal cofinitary group has size at least the cardinality of the smallest non-meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal cofinitary groups may be quite arbitrary.