Functional Analysis - Lancaster

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Functional Analysis Alexander C. R. Belton c Alexander C. R. Belton 2004, 2006. Copyright Hyperlinked and revised edition All rights reserved The right of Alexander Belton to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Contents Contents i Introduction iii 1 Normed Spaces 3. Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Subspaces and Quotient Spaces . . . . . . . . . . . . . . . . . . . . . . 4. Completions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Direct Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Initial Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Exercises 1.

Introduction These notes are an expanded version of a set written for a course given to final-year undergraduates at the University of Oxford. A thorough understanding of the Oxford third-year b4 analysis course (an introduction

  Analysis, Functional, Functional analysis