On the surjectivity of linear transformations - M. Damlakhi; V. Anandam (International Journal of Mathematics and Mathematical Sciences)
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.