Interpolation of Banach lattices. (English) Zbl 0549.46038

Nilsson, Per

Stud. Math. 82, 135-154 (1985).

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

Keywords:

Gustavsson-Peetre construction; Banach lattices; non-negative concave function; interpolation spaces; Ovchinnikovs upper and lower methods; Calderón-Lozanovskij construction