算子理論問題集 (英文) (阿爾及)穆罕默德.希赫姆.莫爾塔德著 9787576704365 【台灣高等教育出版社】

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書名：算子理論問題集 (英文)
ISBN：9787576704365
出版社：哈爾濱工業大學
著編譯者：(阿爾及)穆罕默德.希赫姆.莫爾塔德著
叢書名：國外優秀數學著作原版系列
頁數：xxx
所在地：中國大陸 *此為代購商品
書號：1532733
可大量預訂，請先連絡。

內容簡介 本書是反映20世紀初數學家所發現的一種新的看待傳統素材的工具——巴拿赫空間與希爾伯特空間的運算元理論的英文版專著，中文書名可譯為《運算元理論問題集》。作者穆罕默德·希赫姆·莫爾塔德是阿爾及利亞數學家，任阿爾及利亞奧蘭大學教授。

作者簡介 穆罕默德·希赫姆·莫爾塔德，他是阿爾及利亞數學家，任阿爾及利亞奧蘭大學教授。

目錄 Preface
Notation and Terminology
0 1 Notation
0 2 Terminology
Part 1 EXERCISES ET AL
Chapter 1 Normed Vector Spaces Banach Spaces
1 1 Basics
1 1 1 Definitions and Examples
1 1 2 Operations on Banach Spaces
1 1 3 Convex Sets
1 1 4 LP-Spaces
1 2 True or False: Questions
1 3 Exercises with Solutions
1 4 Tests
1 5 More Exercises
Chapter 2 Bounded Linear Operators on Banach Spaces
2 1 Basics
2 1 1 Basic Definitions
2 1 2 Dual Spaces
2 1 3 The Fourier Transform
2 1 4 Invertibility
2 1 5 Series in Banach Spaces
2 1 6 Neumann Series
2 1 7 Operator-Valued Analytic Functions
2 1 8 The Four Pillars of Functional Analysis
2 2 True or False: Questions
2 3 Exercises with Solutions
2 4 Tests
2 5 More Exercises
Chapter 3 Hilbert Spaces
3 1 Basics
3 1 1 Definitions and Examples
3 1 2 Modes of Convergence of Sequences
3 1 3 Orthogonality
3 1 4 The Closest Point Property and the Projection Theorem
3 1 5 Orthonormal Sets and Basy ana tne rro
3 1 6 Orthogonal Polynomials
3 1 7 Linear Operators on a Hilbert Space
3 1 8 Operator Topologies
3 2 True or False: Questions
3 3 Exercises with Solutions
3 4 Tests
3 5 More Exercises
Chapter 4 Classes of Linear Operators on Hilbert Spaces 99
4 1 Basics
4 1 1 Operator Theory Basics
4 1 2 Cartesian Form
4 1 3 Operator Matrices
4 1 4 A Word on the Invariant Subspace Problem
4 2 True or False: Questions
4 3 Exercises with Solutions
4 4 Tests
4 5 More Exercises
Chapter 5 Positive Operators Square Root
5 1 Basics
5 1 1 Positive Operators
5 1 2 Invertibility Revisited
5 1 3 Square Root of Positive Operators
5 2 True or False: Questions
5 3 Exercises with Solutions
5 4 Tests
5 5 More Exercises
Chapter 6 Absolute Value Polar Decomposition of an Operator
6 1 Basics
6 1 1 Definitions and Properties
6 1 2 The Absolute Value and the Product
6 1 3 The Absolute Value and the Sum
6 1 4 The Absolute Value and Other Inequalities
6 1 5 Polar Decomposition
6 2 True or False: Questions
6 3 Exercises with Solutions
6 4 Tests
6 5 More Exercises
Chapter 7 Spectrum of an Operator
7 1 Basics
7 1 1 Definitions and Properties
7 1 2 The Resolvent Function
7 1 3 Subsets of the Spectrum
7 1 4 Spectrum of the Product of Operators
7 1 5 On The Operator Equation AX - XB = C
7 1 6 Polynomial Calcul-yuawva A
7 2 True or False: Questions
7 3 Exercises with Solutions
7 4 Tests
7 5 More Exercises
Chapter 8 Spectral Radius Numerical Range
8 1 Basics
8 1 1 Spectral Radius
8 1 2 Numerical Range
8 2 True or False: Questions
8 3 Exercises with Solutions
8 4 Tests
8 5 More Exercises
Chapter 9 Compact Operators
9 1 Basics
9 1 1 Compact Operators
9 1 2 Hilbert-Schmidt Operators
9 1 3 Spectrum and Compact Operators
9 2 True or False: Questions
9 3 Exercises with Solutions
9 4 Tests
9 5 More Exercises
Chapter 10 Closed Operators
10 1 Basics
10 1 1 Spectrum
10 1 2 Closedness of Products and Sums
10 1 3 A Word on Distributional Derivatives
10 2 True or False: Questions
10 3 Exercises with Solutions
10 4 Tests
10 5 More Exercises
Chapter 11 Functional Calculi
11 1 Basics
11 1 1 Functional Calculus for Self-adjoint Operators
11 1 2 Functional Calculus for Normal Operators
11 1 3 A Little Digression
11 1 4 The Fuglede-Putnam Theorem Revisited
11 1 5 The Beck-Putnam Theorem
11 2 True or False: Questions

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