Abstract
Let E be a compact subset of G, the union set of nontrivial Gleason parts, and I ( E ) be the associate primary ideal of H ∞ . We give a characterization of the numbering function ord ( I ( E ) , x ) , the zero's order of I ( E ) at x in E, using the geometrical words of E. We also give some factorization theorems of Blaschke products. Using these, we give some descriptions of the higher order hulls of I ( E ) , and for a Carleson–Newman Blaschke product in I ( E ) it is proved that I ( E ) is generated by its subproducts as a closed ideal. When each E i is ρ-separated, we also prove that the tensor product ⊗ i = 1 k I ( E i ) is closed in H ∞ .
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