Metric Projections in Spaces of Integrable Functions Original Research Article

The paper is concerned with the calculation of the derived mapping of the metric projection onto a finite dimensional subspace of a space of integrable functions. Abstract results for quotient spaces and for spaces which are l1-direct sums are obtained and are applied to real or complex spaces of integrable functions to obtain improvements of a number of results of Li for real spaces of integrable functions. Metric projections onto one-dimensional subspaces of spaces of integrable functions are considered and it is shown that there is an essential difference between the real and complex cases.