International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 545-548

On the surjectivity of linear transformations

M. Damlakhi and V. Anandam

Department of Mathematics, King Saud University, P O Box 2455, Riyadh 11451, Saudi Arabia

Received 11 February 1993; Revised 2 March 1993

Copyright © 1996 M. Damlakhi and V. Anandam. 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.


Let B be a reflexive Banach space, X a locally convex space and T:BX (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given vX there is a solution for the equation Tu=v. This result is used to discuss the existence of an Lp-weak solution of Du=v where D is a differential operator with smooth coefficients and vLp.