It is shown that the
complemented subspaces of Lp(μ)-spaces are isomorphically and isometrically
characterized by the behavior of the integral operators defined on such spaces. If the
integral operators from E to any F are exactly those operators naturally inducing
continuous maps from lqE to lqF (where p−1+ q−1= 1), then E is
a ℒp-space or a ℒ2-space. Further, if the integral norm always coincides
with the operator norm of the induced mapping, then E is isometric to an
Lp(μ)-space.
