With an addendum by Wu Congxin (Harbin Institute of Technology)Linear Functional Analysis resulted from a series of lectures Orlicz gave in Beijing, China, 1958. The orignal edition was published in Chinese in 1963. It contains all the major theorems that would normally appear in a modern text, the results of special interest to the Polish school, and others which are not easily available elsewhere. Orlicz provided in this book some rare insight and motivation in the subject which was initiated by the Polish school. An addendum to some recent results in Orlicz spaces is included.
Preliminaries in functional analysis; examples of Banach and Frechet spaces; a unified approach of some useful Banach and Frechet spaces - Orlicz and modular spaces; normed spaces induced by given spaces; equivalent norms and isometry of spaces; convergence in the topological linear spaces; remarks in non-isometry of spaces; unconditionally and absolutely convergent series; linear functionals; separation theorems and their applications; conjugate spaces; continuous operators and operator sequences; some applications to summability theory and orthogonal series; addendum - some recent results in Orlicz spaces; exercises.