## Functional AnalysisThis Book Is An Introductory Text Written With Minimal Prerequisites. The Plan Is To Impose A Distance Structure On A Linear Space, Exploit It Fully And Then Introduce Additional Features Only When One Cannot Get Any Further Without Them. The Book Naturally Falls Into Two Parts And Each Of Them Is Developed Independently Of The Other The First Part Deals With Normed Spaces, Their Completeness And Continuous Linear Maps On Them, Including The Theory Of Compact Operators. The Much Shorter Second Part Treats Hilbert Spaces And Leads Upto The Spectral Theorem For Compact Self-Adjoint Operators. Four Appendices Point Out Areas Of Further Development.Emphasis Is On Giving A Number Of Examples To Illustrate Abstract Concepts And On Citing Varirous Applications Of Results Proved In The Text. In Addition To Proving Existence And Uniqueness Of A Solution, Its Apprroximate Construction Is Indicated. Problems Of Varying Degrees Of Difficulty Are Given At The End Of Each Section. Their Statements Contain The Answers As Well. |

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Hai my name is Abhijith,iam from kerala,India.This book was very useful to me for completing my project in the topic "Normed Spaces"...

### Contents

Preliminaries | 1 |

Fundamentals of Normed Spaces | 62 |

Bounded Linear Maps on Banach Spaces | 138 |

Spaces of Bounded Linear Functionals | 216 |

Compact Operators on Normed Spaces | 302 |

Geometry of Hilbert Spaces | 367 |

Bounded Operators on Hilbert Spaces | 441 |

Appendix A Fixed Points | 528 |

Appendix B Extreme Points | 541 |

SturmLiouville Problems | 553 |

Unbounded Operators and Quantum Mechanics | 571 |

Bibliography | 591 |

List of Symbols | 597 |

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### Common terms and phrases

assume Banach space basis for H best approximation BL(H BL(X bounded operator bounded sequence bounded subset Cauchy sequence CL(X closed subspace closure compact operator consider continuous function convergent subsequence convex subset countable define denote dm(t eigenvalue eigenvector element example F(xn finite dimensional finite rank follows Fredholm integral operator given Hahn-Banach extension Hence Hilbert space Hint inequality inner product space invertible isometry kernel Lebesgue Lemma Let F Let H Let xn linear map linear space linearly independent map F measurable function metric space nonempty closed nonzero normed space operator on H orthonormal basis orthonormal set polynomial positive integer Problem Proof real numbers reflexive resp result scalar Schauder basis Section self-adjoint operator sequence xn shows solution spaces and F span subspace surjective Theorem Let totally bounded uniformly unique weak convergence

### References to this book

Spectral Computations for Bounded Operators Mario Ahues,Alain Largillier,Balmohan Limaye No preview available - 2001 |