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Operators on Lp (2 < p < ∞) which factor through Xp

Author:
Bentuo Zheng  


Journal:
Journal of Functional Analysis


Issue Date:
2017


Abstract(summary):

Abstract Let T be a bounded linear operator on L p ( 2 < p < ∞ ) . We show that T factors through X p if and only if there is a change of density of L p so that the induced operator T ˜ satisfies an upper- ℓ p ⊕ ℓ 2 -tree estimate. An operator which factors through X p but fails the upper- ℓ p ⊕ ℓ 2 -tree estimate is constructed. It is also shown that if T is a closed Z p -strictly singular operator on L p ( 2 < p < ∞ ) , then T factors through X p . However, there exists a Z p -strictly singular operator which does not factor through X p .


Page:
782-782


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