Interpolation of Banach lattices
Copyright policy )Interpolation of Banach lattices
For each couple \(\bar X=(X_ 0,X_ 1)\) of Banach lattices and each non- negative concave function \(\phi\) let \(\) 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.
Banach lattices, non-negative concave function, Calderón-Lozanovskij construction, interpolation spaces, Abstract interpolation of topological vector spaces, Gustavsson-Peetre construction, Ovchinnikovs upper and lower methods
Banach lattices, non-negative concave function, Calderón-Lozanovskij construction, interpolation spaces, Abstract interpolation of topological vector spaces, Gustavsson-Peetre construction, Ovchinnikovs upper and lower methods
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