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Two remarks on primary spaces

Published online by Cambridge University Press:  07 June 2012

Institut für Analysis, J. Kepler Universität, A-4040 Linz, Austria. e-mail:


We prove that for an operator T on ℓ(H1 ()), respectively ℓ(L1 ()), the identity factors through T or Id - T. Hence ℓ(H1 ()) and ℓ(L1 ()) are primary spaces. We re-prove analogous results of H.M. Wark for the spaces ℓ(Hp()), 1 < p < ∞. In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemerédi's theorem in [11].

Research Article
Copyright © Cambridge Philosophical Society 2012

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