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Metrics, Norms, Inner Products, and Operator Theory by Christopher Heil

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Metrics, Norms, Inner Products, and Operator Theory written by Christopher Heil
This text is an introduction to the main types of spaces that pervade analysis. These are metric spaces, normed spaces, and inner product spaces (all of which are particular types of an even more general class of sets known as topological spaces). Essentially, a metric space is a set on which we can define a notion of “distance,” or “metric,” between points in the set. Normed spaces are metric spaces, but the concept of a normed space is more restrictive, in two respects. First, a normed space must be a vector space (and hence there is a way to add vectors together, and to multiply a vector by a scalar). Second, the existence of a norm not only provides us with a way to measure the distance between vectors, but also gives each individual vector in the space a “length.” Inner product spaces have an even more restrictive definition, because each pair of vectors must be assigned an inner product, which in essence tells us the “angle” between these vectors. The Euclidean space Rd and its complex analogue Cd are familiar examples of inner product spaces. We will introduce and study metrics, norms, and inner products in this text, as well as operators that transform one such space into another space.
(Christopher Heil)

Book Detail :-
Title: Metrics, Norms, Inner Products, and Operator Theory
Edition:
Author(s): Christopher Heil
Publisher: Birkhauser,Birkha¨user
Series: Applied and Numerical Harmonic Analysis
Year: 2018
Pages: 374
Type: PDF
Language: English
ISBN: 978-3-319-65322-8,3319653229,978-3-319-65321-1
Country: US

Author Christopher Heil is from Georgia Institute of Technology since 1993. His teaches calculus, linear algebra, analysis, and abstract algebra. He is an experienced author, teacher and served as a consultant on the previous edition of this text. He is researcher in harmonic analysis, including time-frequency analysis, wavelets, and operator theory.

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Book Contents :-
Metrics, Norms, Inner Products, and Operator Theory written by Christopher Heil cover the following topics.
Preface
1. Notation and Preliminaries
2. Metric Spaces
3. Norms and Banach Spaces
4. Further Results on Banach Spaces
5. Inner Products and Hilbert Spaces
6. Operator Theory
7. Operators on Hilbert Spaces
Index of Symbols
References
Index

Note:-

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