## Linear Operators: General theory |

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space implies inequality integral interval isomorphism L₁ L₁(S Lebesgue Lemma limit linear functional linear operator linear space mapping Math means measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset sufficient Suppose Theorem theory topology transformations uniform uniformly unique valued vector weak weakly compact zero