## Linear Operators: General theory |

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Page 96

... to introduce the symbol A - B to denote the set An B ' . However , this notation

will be avoided whenever S is a group and there is possibility of confusion with

the group operation . We will use the notation A A B for the

A ...

... to introduce the symbol A - B to denote the set An B ' . However , this notation

will be avoided whenever S is a group and there is possibility of confusion with

the group operation . We will use the notation A A B for the

**symmetric**difference (A ...

Page 156

... A A E ) = 0 , where A A E is the

The fact that ~ is an equivalence relation follows readily from the fact that the

... A A E ) = 0 , where A A E is the

**symmetric**difference ( A U E ) - AE of A and E .The fact that ~ is an equivalence relation follows readily from the fact that the

**symmetric**difference is a commutative and associative operation with A A A = 0 .Page 813

The expansion problems associated with regular differential systems of the

second order . Trans . Amer . Math . Soc . 29 , 826 - 844 ( 1927 ) . Štraus , A . V . 1

. On the theory of the generalized resolvent of a

Akad .

The expansion problems associated with regular differential systems of the

second order . Trans . Amer . Math . Soc . 29 , 826 - 844 ( 1927 ) . Štraus , A . V . 1

. On the theory of the generalized resolvent of a

**symmetric**operator . DokladyAkad .

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

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### Common terms and phrases

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero