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On the surjectivity of linear transformations

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  • M. Damlakhi
  • V. Anandam

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 T u = v . This result is used to discuss the existence of an L p -weak solution of D u = v where D is a differential operator with smooth coefficients and v ∈ L p .

Suggested Citation

  • M. Damlakhi & V. Anandam, 1996. "On the surjectivity of linear transformations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:587092
    DOI: 10.1155/S0161171296000750
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