International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 7, Pages 487-492
doi:10.1155/S0161171200002465

New characterizations of some Lp-spaces

Russell S. Jenkins1 and Ramesh V. Garimella2

1American General Life and Accident Insurance Company, 450S American General Center, Nashville 37250, TN, USA
 2Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville 38505, TN, USA

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.