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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Projections onto translation-invariant subspaces of $ H\sp 1({\bf R})$


Authors: Dale E. Alspach and David C. Ullrich
Journal: Trans. Amer. Math. Soc. 313 (1989), 571-588
MSC: Primary 43A15
MathSciNet review: 974510
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Abstract: Recently I. Klemes has characterized the complemented translation-invariant subspaces of $ {H^1}(\mathbb{T})$. In this paper we investigate the case of $ {H^1}(\mathbb{R})$. The main results are that the hull of a complemented translation-invariant subspace is $ \varepsilon $-separated for some $ \varepsilon > 0$, and that an $ \varepsilon $-separated subset of $ {\mathbb{R}^ + }$ which is in the ring generated by cosets of closed subgroups of $ \mathbb{R}$ (intersected with $ {\mathbb{R}^ + }$) and lacunary sequences is the hull of a complemented ideal.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0974510-2
Article copyright: © Copyright 1989 American Mathematical Society