Banach Function Lattices Research Articles

Interpolation theorem for linear operators

In generalizing a series of known results, the following theorem is proved: If K is a continuous linear operator mapping E0 into F0 and E1 into F1 (where E0, E1 and F0, F1, being ideal spaces, are Banach lattices of functions defined on Ω1 and Ω2 respectively), then for any λ. e (0, 1) K maps E 0 1−λ E 1 λ into [(F 0 ′ )1−λ(F 1 ′ )λ]′ and is continuous; for suitably chosen norms in the spacesE 0 1−λ E 1 λ and [(F 0 ′ )1−λ(F 1 ′ )λ] the norm of K is a logarithmically convex function of λ. Six titles are cited in the bibliography.