International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 31-35
doi:10.1155/S0161171200001721
On the extension of positive linear functionals
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.
Abstract
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.