|
|
M. FABIAN, P. HABALA, P. HAJEK, J. PELANT,
V. MONTESINOS and V. ZIZLER: Functional Analysis and Infinite
Dimensional Geometry. CMS Books in
Mathematics 8. Canadian Mathematical
Society. Springer Verlag. 2001. ISBN 0-387-95219-5.
A sample (Title,
Foreword, Table of Contents, References, Index)
Link to the
Springer-Verlag Homepage
Excerpts from some Reviews.
Mathematical Review 1831176 (2002f:46001): ``This is a
substantial text containing an up-to-date exposition of functional
analysis from a Banach space point of view. It will be particularly
useful for research investigation of nonlinear functional analysis
and optimization (...) and the last five chapters introduce the
reader to the latest research frontiers in the theory of Banach
spaces specially related to differentiability of norms and topology
(...) It is usefully balanced with a complementary section on
extremal structure of sets (...) Chapter 9 is a useful
exposition of research (...) This chapter brings the reader to view
where recent research action has taken place (...) and the
fine exposition (...) deals with recent significant work (...) an
introduction to the latest research (...) Each chapter ends with a
remarkably weighty collection of exercises, many of which have
useful hints at solutions appended to them (one chapter has 111
exercises!) (...) the reader is directed throughout to the ample
collection of references. This book will stand as an important
working text and reference and a significant guide for research
students". Reviewed by John R. Giles. Copyright American
Mathematical Society 2002, 2007.
"The sextet of authors have done a superb job in marshalling and
presenting their material: the writing is crisp and authoritative
and they take full advantage of recent simplifications in the proofs
of certain results. The fulsome, up-to-date bibliography is
accompanied by a marvellous collection of nearly 700 exercises
(with integrated hints): for both learners and lecturers, this rich
source of material alone is worth more than the cost of the book.
\`{a} I warmly commend this book \`{a} ." (Nick Lord, The
Mathematical Gazette, Vol. 87 (509), 2003)
"This book, which contains a vast amount of material, is intended
as an introduction to linear function analysis . At the end of each
chapter there is a wealth of beautiful applications and exercises .
I would highly recommend this book to anyone interested in the study
of Banach spaces. I think it would be fair to say that if one knew
half of the material contained in this book, then one would know
quite a lot." (Warren Moors, The Australian Mathematical Society
Gazette, Vol. 29 (5), 2002).
"This book is based on graduate courses taught at the university
of Alberta in Edmonton. It is intended as an introduction to linear
functional analysis and to some parts of infinite-dimensional Banach
space theory. It is full of facts, theorems, corollaries; along with
a large number of exercises with detailed hints for their solution.
\`{a} The authors have accomplished a text which is easily readable
and as self-contained as possible. A very excellent book for the
topics covered!" (Joe Howard, Zentralblatt MATH, Vol. 981, 2002)
|