On the surjectivity of linear transformations
M. Damlakhi, Victor Anandam · International Journal of Mathematics and Mathematical Sciences · 1993
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.