New characterizations of some Lp-spaces

Abstract

For a complete measure space (X,∑,μ), we give conditions which force Lp(X,μ), for 1≤p<∞, to be isometrically isomorphic to ℓp(Γ) for some index set Γ which depends only on (X,μ). Also, we give some new characterizations which yield the inclusion Lp(X,μ)⊂Lq(X,μ) for 0<p<q.