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Series Preface vii 1 Linear Spaces 1
 

Summary: Contents
Series Preface vii
Preface ix
1 Linear Spaces 1
1.1 Linear spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Normed spaces . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Convergence . . . . . . . . . . . . . . . . . . . . . . 10
1.2.2 Banach spaces . . . . . . . . . . . . . . . . . . . . . 13
1.2.3 Completion of normed spaces . . . . . . . . . . . . . 15
1.3 Inner product spaces . . . . . . . . . . . . . . . . . . . . . . 22
1.3.1 Hilbert spaces . . . . . . . . . . . . . . . . . . . . . . 27
1.3.2 Orthogonality . . . . . . . . . . . . . . . . . . . . . . 28
1.4 Spaces of continuously differentiable functions . . . . . . . 39
1.4.1 H¨older spaces . . . . . . . . . . . . . . . . . . . . . . 41
1.5 Lp
spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.6 Compact sets . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2 Linear Operators on Normed Spaces 51
2.1 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2 Continuous linear operators . . . . . . . . . . . . . . . . . . 55

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences