The present book is the first of four books that we intend to publish. The uniqueness of this publication lies in the fact that it contains the general problems and questions Grigorii Yakovlevich Lozanovsky himself set through the last 16 years of his life (It should be born in mind that he died in 1976 barely 39 years old'.). He left 25 note-books with 2223 problems and questions (as well as remarks) dealing mainly with various fields of functional analysis. Many of these questions were answered during the lifetime of Lozanovsky by himself and other mathematicians; a part of these answers can be find in the survey papers of AN. Bukhvalov, A.L Veksler, and G.Ya. Lozanovsky [L59], and AN. Bukhvalov, A.I. Veksler and V.A. Geyler [21] published in 1979 and 1980, respectively.
The conference "Function Spaces V" that took place in 1998, in Poznań, Poland, and where one day was devoted to the occasion of the 60th anniversary of G.Ya. Lozanovsky's birth, showed there was great interest in his work (see [ą7]) and had a decisive influence on the need felt to publish this book.
The book deals with 609 questions, problems, and remarks from the first three of Lozanovsky's note-books. We have omitted the problems crossed out or having evidently obvious answers (which had been noticed by the author himself) but left the original numeration of items. Some remarks in reference to these problems and the classification of them was made in 1977 by Professor A.I. Veksler; we have included them in the book without any changes. At the end of this book we present the full list of publications by G.Ya. Lozanovsky, as well as a list of other publications quoted in the new comments, which we designate as [LI], [L2], etc. and [1], [2], etc., respectively.

Contents:

Preface of the Editors
Notations and terminology
Note-book I (problems 4-298)
Note-book II (problems 299-480)
Note-book III (problems 481-609)
Remarks to G.Ya. Lozanovsky's problems made by A.L Vehsler in the summer of 1977 at the suburban estate Dubovka, near Voronezh, Russia
The thematic classification of G.Ya. Lozanovsky's problems from his note-books I, II, III made by A.I. Veksler in 1977
List of publications of Grigorii Ya. Lozanovsky
Other papers quoted in this book
Author index
Sample pages from G. Ya. Lozanovsky's original text