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Interpolation of Banach lattices. (English) Zbl 0549.46038
For each couple $$\bar X=(X_ 0,X_ 1)$$ of Banach lattices and each non- negative concave function $$\phi$$ let $$<\bar X,\phi>$$ and $$\phi(\bar X)$$ denote the $$\pm$$ interpolation spaces of Gustavsson-Peetre respectively the Calderón-Lozanovskij construction. In this note we show that these spaces essentially coincide. Further we describe the interpolation spaces generated by Ovchinnikovs upper and lower methods in terms of the Calderón-Lozanovskij construction.

##### MSC:
 46M35 Abstract interpolation of topological vector spaces 46B42 Banach lattices
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