Projections onto translation-invariant subspaces of 𝐻¹(𝑅)

Alspach, Dale E.; Ullrich, David C.

doi:10.1090/S0002-9947-1989-0974510-2

Projections onto translation-invariant subspaces of $H^ 1(\textbf {R})$
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by Dale E. Alspach and David C. Ullrich PDF

Trans. Amer. Math. Soc. 313 (1989), 571-588 Request permission

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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Separating sets with the Fourier-Stieltjes transform

Linear operators

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