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**Linear functional analysis. Transl. from the Chinese by Lee Peng Yee. Addendum by Wu Congxin.**
*(English)*
Zbl 0799.46002

Series in Real Analysis. 4. Singapore: World Scientific. xvi, 246 p. (1992).

Professor W. Orlicz has delivered in 1958 a series of lectures on selected chapters of functional analysis at the Mathematical Institute of Academia Sinica, Peking. His lectures, together with various exercises, selected by A. Pelczyński (who accompanied Orlicz to China), have been translated by his Chinese colleagues and students (from German) into Chinese and published in Peking, 1963, with a preface of Orlicz. This work has very much influenced the subsequent development of functional analysis in China, and now his Chinese colleagues and students are presenting this work to the world’s mathematical community in English. The translation is due to Lee Peng Yee (Nat. Univ. Singapore), and an important “Addendum” by Wu Congxin (Harbin Inst. of Technology) provides new information on later developments of the theory of Orlicz spaces. They had the permission of the author, who, unfortunately, deceased in 1990, so he could not see the completion of his book.

In the Preface, written by Prof. Julian Musielak, it is justly stated that the book is “written in a fresh and charming way and it is obvious to the reader that the author was deeply involved in the creation of most of what he describes”. “The contents ... present the point of view of great contributors to functional analysis from Lwów, and of W. Orlicz and S. Mazur, whose collaboration led to many results presented in the book.”

But the book is not only a history. Many of the results form a living mathematics up to today, presented by a great master.

In the Preface, written by Prof. Julian Musielak, it is justly stated that the book is “written in a fresh and charming way and it is obvious to the reader that the author was deeply involved in the creation of most of what he describes”. “The contents ... present the point of view of great contributors to functional analysis from Lwów, and of W. Orlicz and S. Mazur, whose collaboration led to many results presented in the book.”

But the book is not only a history. Many of the results form a living mathematics up to today, presented by a great master.

Reviewer: B.Sz.-Nagy (Szeged)

### MSC:

46-02 | Research exposition (monographs, survey articles) pertaining to functional analysis |

46-03 | History of functional analysis |

46Bxx | Normed linear spaces and Banach spaces; Banach lattices |

01A60 | History of mathematics in the 20th century |