International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 545-548
doi:10.1155/S0161171296000750
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
Abstract
Let B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given v∈X 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 v∈Lp.