## Linear Operators, Part 2 |

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Page 1837

On a calculus of operators in

45 , 217 - 234 ( 1939 ) . 3 . The Cauchy - Schwarz inequality and self - adjoint

spaces . Ann . of Math . ( 2 ) 46 , 468 – 473 ( 1945 ) . 4 . On certain implications ...

On a calculus of operators in

**reflexive**vector spaces . Trans . Amer . Math . Soc .45 , 217 - 234 ( 1939 ) . 3 . The Cauchy - Schwarz inequality and self - adjoint

spaces . Ann . of Math . ( 2 ) 46 , 468 – 473 ( 1945 ) . 4 . On certain implications ...

Page 1917

( See also Factor ) space , ( 38 ) Real vector space , ( 38 ) , ( 49 ) Rectifiable

curve , ( 225 )

425 ) definition , II . 3 . 22 ( 66 ) discussion , ( 88 ) examples of

.

( See also Factor ) space , ( 38 ) Real vector space , ( 38 ) , ( 49 ) Rectifiable

curve , ( 225 )

**Reflexivity**, alternate proof , V . 7 . 11 ( 436 ) criterion for , V . 4 . 7 (425 ) definition , II . 3 . 22 ( 66 ) discussion , ( 88 ) examples of

**reflexive**space , IV.

Page 1923

18 - 14 ( 295 - 296 ) of

, V . 4 relations with separability and metrizability , V . 5 study of fundamental

properties , V . 3 weak compactness , V . 6 weak operator topology , definition , VI

.

18 - 14 ( 295 - 296 ) of

**reflexive**spaces , II . 3 . ... 3 ( 427 ) relations with**reflexivity**, V . 4 relations with separability and metrizability , V . 5 study of fundamental

properties , V . 3 weak compactness , V . 6 weak operator topology , definition , VI

.

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero