International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 31-35

On the extension of positive linear functionals

Ergashboy Muhamadiev1 and Adel T. Diab2

1Mathematical and Informational Department, Khujand's Scientific Center, Academy of Sciences, P.O. 3 Box 113, Khujand, Tajikistan
2Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt

Received 12 September 1997; Revised 20 April 1998

Copyright © 2000 Ergashboy Muhamadiev and Adel T. Diab. 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.


A necessary and sufficient condition to extend a continuous linear real functionals which is positive with respect to a semi-group defined on a subspace of a linear space is discussed in this paper. The case of a closed subspace of a Banach space is also discussed.