Two Remarks on Primary Spaces
Paul F.X. Mueller

TL;DR
This paper investigates the factorization properties of operators on certain Banach spaces, proving that the identity operator factors through any operator or its complement, and offers combinatorial proofs replacing previous reliance on Szemeredi's theorem.
Contribution
It extends factorization results to spaces (H^p(T)) for 1<p<, using combinatorics of dyadic intervals instead of Szemeredi's theorem.
Findings
Identity factors through any operator or its complement on (H^1(T)).
Analogous results are established for (H^p(T))) spaces for 1<p<.
Combinatorial methods replace the dependence on Szemeredi's theorem.
Abstract
We prove that for any operator on , the identity factores through or . We re-prove analogous results of H.M. Wark for the spaces , . In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemeredi's theorem in the work of H. M. Wark.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods
