- 128 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
A First Course in Functional Analysis
About this book
This introduction to functional analysis is based on the lecture notes of Martin Davis, a distinguished professor of mathematics. The treatment demonstrates the essential unity of mathematics without assuming more background than can be expected of advanced undergraduates and graduate students majoring in mathematics.
A self-contained exposition of Gelfand's proof of Wiener's theorem, this volume explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. Numerous problems appear throughout the book.
A self-contained exposition of Gelfand's proof of Wiener's theorem, this volume explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. Numerous problems appear throughout the book.
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Yes, you can access A First Course in Functional Analysis by Martin Davis in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.
Information
CHAPTER 1
Set Theoretic Preliminaries
1. Sets and Members
In this section the terms class, set, collection, totality and family will be used synonomously. The symbol, ∈(epsilon), will be used to denote membership in a class. The symbol, ∉, will denote non-membership in a class, i.e.,
x ∈ C means x is a member of set C
x ∉ C means x is not a member of set C
Example: If C is the class of all even numbers, then 2 belongs to C, (2 ∈ C), 4 belongs to C, (4 ∈ C), and 3 does not belong to C, (3 ∉ C).
If a set is finite, then it can be described by listing its members. For example:
Let C be the set {1, 3, 5} then 1 ∈ C, 3 ∈ C, 5 ∈ C and all other elements are not members of the set C. The description of an infinite set, however, is not so simple. An infinite set can not be described by simply listing its elements. Hence, we must have recourse to defining the set by a characteristic property. The set can then be described as the set of all elements which possess the property in question. If the property is, say, P(x), then the set will be written {x | P(x)}, thus to write C = {...
Table of contents
- Cover
- Title Page
- Contents
- Copyright Page
- 1. Set Theoretic Preliminaries
- 2. Normed Linear Spaces and Algebras
- 3. Functions on Banach Spaces
- 4. Homomorphisms on Normed Linear Spaces
- 5. Analytic Functions into a Banach Space
- Index