• Title/Summary/Keyword: left $\gamma$-factorable polynomial

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POLYNOMIAL FACTORIZATION THROUGH Lγ(μ) SPACES

  • Cilia, Raffaella;Gutierrez, Joaquin M.
    • Journal of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1293-1307
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    • 2009
  • We give conditions so that a polynomial be factorable through an $L_{\gamma}({\mu})$ space. Among them, we prove that, given a Banach space X and an index m, every absolutely summing operator on X is 1-factorable if and only if every 1-dominated m-homogeneous polynomial on X is right 1-factorable, if and only if every 1-dominated m-homogeneous polynomial on X is left 1-factorable. As a consequence, if X has local unconditional structure, then every 1-dominated homogeneous polynomial on X is right and left 1-factorable.