Classical Banach spaces. 1: Sequence spaces. 2. Function spaces. Repr. of the 1977 and 1979 ed. (English) Zbl 0852.46015

Lindenstrauss, Joram; Tzafriri, Lior

Classics in Mathematics. Berlin: Springer-Verlag. xx, 432 p. (1996).

The book has been written in the middle of the seventies by brilliant mathematicians, professors of Hebrew University of Jerusalem Joram Lindenstrauss and Lior Tzafriri. Starting their work they planned to write 4 volumes, but unfortunately the last two of them had not appeared. In spite of this the first and second volumes (which are edited now as one book) cover the most important branches of the Banach space theory. Now, this book is the best manual of the subject, and the first word of its title (“classical”) can be applied also for the book itself and for scientific results of its authors too.
A detailed description of the book contents may be found in the reviews of the first edition: Zbl 0362.46013 (Vol. 1, 1997) and Zbl 0403.46022 (Vol. 2, 1979).

Reviewer: M.I.Kadets (Khar’kov)

MSC:

46B20	Geometry and structure of normed linear spaces
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46B42	Banach lattices
46B45	Banach sequence spaces

Keywords:

Banach space; Banach lattice; Schauder basis; uniform convexity; Boyd indices

Citations:

Zbl 0362.46013; Zbl 0403.46022