Vol. 46, No. 2, 1973

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Integral operators on p-spaces

Daniel Ralph Lewis

Vol. 46 (1973), No. 2, 451–456
Abstract

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 lq ∨
⊗ E to lq∧
⊗ F (where p1 + q1 = 1), then E is a p-space or a 2-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.

Mathematical Subject Classification 2000
Primary: 47B10
Milestones
Received: 25 April 1972
Published: 1 June 1973
Authors
Daniel Ralph Lewis