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Geometry of linear 2-normed spaces. (English) Zbl 1051.46001
Huntington, NY: Nova Science Publishers (ISBN 1-59033-019-6). 301 p. $ 95.00 (2001).
The purpose of this book is to give a comprehensive introduction to the study of 2-metric spaces and linear 2-normed spaces. It consists of two Chapters with Chapter one as an introduction. Chapters 2 and 3 give the basic definitions of an 2-metric space and a linear 2-normed space and introduces the topology generated by a 2-metric. Chapters 4 and 5 deal with the completion problem leading to the notion of a 2-Baanch space, and analoguously, the notion of 2-inner product leads to 2-Hilbert spaces. Chapters 6, 7, and 8 study the notion of convexity in linear 2-normed spaces. Chapter 9 generalizes the previous results and produces an example of a nonlinear isometry. Chapter 10 introduces an orthogonality relation for norme linear spaces. Finally, Chapter two generalizes the notion of a real 2-inner space by using the concept of quadratic forms.
46-00Reference works (functional analysis)