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Two remarks on primary spaces

Published online by Cambridge University Press:  07 June 2012

PAUL F. X. MÜLLER
PAUL F. X. MÜLLER*
Affiliation:
Institut für Analysis, J. Kepler Universität, A-4040 Linz, Austria. e-mail: pfxm@bayou.uni-linz.ac.at
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Abstract

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].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 3 , November 2012 , pp. 505 - 523
Copyright
Copyright © Cambridge Philosophical Society 2012

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References

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