Transactions of the American Mathematical Society

Author(s): Jun-ichi Tanaka
Journal: Trans. Amer. Math. Soc. 348 (1996), 4113-4129.
MSC (1991): Primary 46J10, 46J15, 43A17; Secondary 30H05, 54H20
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Abstract: Using the Stone-\v{C}ech compactification $\beta \mathbf Z$ of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces $H^p(\mu )$ , $1\le p\le \infty$ , the corresponding subspaces $H_0^p(\mu )$ are all singly generated. This shows the existence of maximal weak- $^*$

Dirichlet algebras, different from $H^\infty$ of the disc, for which the single generator problem is settled.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46J10, 46J15, 43A17, 30H05, 54H20

Jun-ichi Tanaka
Affiliation: Department of Mathematics, Tsuru University, Tsuru City, Yamanashi 402, Japan

DOI: 10.1090/S0002-9947-96-01566-8
PII: S 0002-9947(96)01566-8
Keywords: Ergodic Hardy spaces, outer functions, single generators, cocycles
Received by editor(s): February 3, 1994
Received by editor(s) in revised form: May 24, 1995
Additional Notes: This research was partially supported by Grants 03640174, 04640183 and 05640221 from the Japanese Ministry of Education
Dedicated: Dedicated to Professor Yuji Ito on his 60th birthday
Copyright of article: Copyright 1996, American Mathematical Society

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