2016
DOI: 10.1002/mana.201600244
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How do the positive embeddings of Banach lattices depend on the αth derivatives of K?

Abstract: Let K and S be locally compact Hausdorff spaces and X be an abstract Lp space. Suppose that T is a positive Banach lattice isomorphism from COfalse(Kfalse) into COfalse(S,Xfalse). Then for each ordinal α the cardinalities of the αth derivatives Kfalse(αfalse) and Sfalse(αfalse) satisfy the following inequality ||K(α)1/p≤false∥Tfalse∥T−1||S(α)1/p.Moreover, if false∥Tfalse∥T−1<21/p,then Kfalse(αfalse) is a continuous image of a subset of Sfalse(αfalse) which can be taken closed when K is compact. The first state… Show more

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