Christopher E. Heil

School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
(404) 894-9231
h e i l @ m a t h . g a t e c h . e d u

C. Heil:   METRICS, NORMS, INNER PRODUCTS, AND OPERATOR THEORY, Birkhäuser/Springer, Cham, 2018 (xxi + 359 pp.).

Mathematics deals with many types of objects---shapes, numbers, points in Euclidean space, functions, linear transformations, graphs, to name only a few. However, these objects do not exist in isolation, and by looking at the properties of a related family or space of objects we often gain new understanding. In analysis, which in many ways is the "science of functions", the three main types of families that we encounter are metric spaces, normed spaces, and inner product spaces. This text is a self-contained introduction to these spaces, and to the operators that transform objects in one space (which are often themselves functions) into objects in another space. The intended reader of this text is a motivated student who is ready to take an upper-level, proof-based undergraduate mathematics course. No knowledge of measure theory or advanced real analysis is required.


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