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
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
Received 5 October 1998
Copyright © 2000 Russell S. Jenkins and Ramesh V. Garimella. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.