## Linear Operators, Part 1 |

### From inside the book

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Page 733

Trans . Amer . Math . Soc . 61 , 122 – 127 ( 1947 ) . 4 . Spectral resolution of

groups of unitary operators .

and Kakutani , S . 1 . Bohr compactifications of a locally compact abelian group , I

, II .

Trans . Amer . Math . Soc . 61 , 122 – 127 ( 1947 ) . 4 . Spectral resolution of

groups of unitary operators .

**Duke Math**. J . 11 , 589 - 595 ( 1944 ) . Anzai , H . ,and Kakutani , S . 1 . Bohr compactifications of a locally compact abelian group , I

, II .

Page 773

3 2 . Banach spaces with the extension property . Trans . Amer . Math . Soc . 72 ,

323 – 326 ( 1952 ) . The Tychonoff product theorem implies the axiom of choice .

Fund . Math . 37 , 75 – 76 ( 1950 ) . 4 . Convergence in topology .

3 2 . Banach spaces with the extension property . Trans . Amer . Math . Soc . 72 ,

323 – 326 ( 1952 ) . The Tychonoff product theorem implies the axiom of choice .

Fund . Math . 37 , 75 – 76 ( 1950 ) . 4 . Convergence in topology .

**Duke Math**.Page 780

second order . J . London Math . Soc . 27 , 33 ... Math . 9 , 37 - 44 ( 1927 ) .

Lengyel , B . A . 1 . On the spectral theorem of self - adjoint operators . Acta Sci .

Math .

**Duke Math**. J . 17 , 57 - 62 ( 1950 ) . 4 . On self - adjoint differential equations ofsecond order . J . London Math . Soc . 27 , 33 ... Math . 9 , 37 - 44 ( 1927 ) .

Lengyel , B . A . 1 . On the spectral theorem of self - adjoint operators . Acta Sci .

Math .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero