International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 241-254

Linear functionals on Orlicz sequence spaces without local convexity

Marian Nowak

Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, Poznań 60-769, Poland

Received 8 March 1990

Copyright © 1992 Marian Nowak. 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.


The general form of continuous linear functionals on an Orlicz sequence space 1ϕ (non-separable and non-locally convex in general) is obtained. It is proved that the space hϕ is an M-ideal in 1ϕ.