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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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