Characterizations of inner product spaces
This is an excellent, selfcontained, up-to-date, exhaustive survey on various isometric characterizations of inner product spaces. In Chapter 2 on 2-dimensional characterizations the author discusses among others James and Birkhoff orthogonality characterizations as well as norm derivatives and best approximation characterizations. In Chapter 3 on 3-dimensional characterizations the characterizations included range from classical Kakutani's result, through metric projections characterizations to Chebyshev centers and proximinal maximal subspaces, to name just a few topics covered in the book. The book is well written, well organized. It bears a seal of expertize of the author who is a renowned specialist in the theory of normed spaces. The book will certainly be a useful source for researchers both in this area as well as in many related areas of functional analysis, geometry and approximation theory.
isometric characterizations of inner product spaces
scientific article; zbMATH DE number 4000736