This is an announcement for the paper "Two remarks on primary spaces" by Paul F.X. Mueller.

Abstract: We prove that for any operator $T$ on $ \ell^\infty( H^1 (\bT)) ,$ the identity factores through $ T $ or $ \Id - T .$ We re-prove analogous results of H.M. Wark for the spaces $ \ell^\infty(H^p(\bT) ), $ $1<p <\infty .$ In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemeredi's theorem in the work of H. M. Wark. \

Archive classification: math.FA

Mathematics Subject Classification: 46B25, 46E40

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Submitted from: pfxm@bayou.uni-linz.ac.at

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