## Linear Operators, Part 1 |

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Page 462

Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by induction

. The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in the

separable case by

256 ) .

Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by induction

. The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in the

separable case by

**Banach**[ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p .256 ) .

Page 810

Weak compactness in

Skorohod , A . ( see Kostyučenko , A . ) Slobodyanskiĩ , M . G . 1 . On estimates for

the eigenvalues of a self - adjoint operator . Akad . Nauk SSSR . Prikl . Mat . Meh .

Weak compactness in

**Banach**spaces . Studia Math . 11 , 71 - 94 ( 1950 ) .Skorohod , A . ( see Kostyučenko , A . ) Slobodyanskiĩ , M . G . 1 . On estimates for

the eigenvalues of a self - adjoint operator . Akad . Nauk SSSR . Prikl . Mat . Meh .

Page 815

Proof of a theorem of Thorin . Bull . Amer . Math . Soc . 50 , 279 – 282 ( 1944 ) .

Taylor , A . E . ( see also Bochner , S . ) 1 . The extension of linear functionals .

Duke Math . J . 5 , 538 - 547 ( 1939 ) . 2 . The weak topologies of

Proof of a theorem of Thorin . Bull . Amer . Math . Soc . 50 , 279 – 282 ( 1944 ) .

Taylor , A . E . ( see also Bochner , S . ) 1 . The extension of linear functionals .

Duke Math . J . 5 , 538 - 547 ( 1939 ) . 2 . The weak topologies of

**Banach**spaces .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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