## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 87

Page 373

This generalizes and abstracts a result

0 , 1 ] by E . Fischer [ 2 ] . The fact that a linear manifold which is not dense in the

entire space has a non - zero orthogonal complement (

This generalizes and abstracts a result

**proved**for closed linear manifolds in L2 [0 , 1 ] by E . Fischer [ 2 ] . The fact that a linear manifold which is not dense in the

entire space has a non - zero orthogonal complement (

**proved**in 4 . 4 ) was ...Page 385

27 . They are essentially due , at least in the real case , to Stone [ 1 ] , although

his terminology and proofs often differ from that given here . It should be

mentioned that Theorem 6 . 22 was

slightly later .

27 . They are essentially due , at least in the real case , to Stone [ 1 ] , although

his terminology and proofs often differ from that given here . It should be

mentioned that Theorem 6 . 22 was

**proved**independently by Cech [ 1 ] onlyslightly later .

Page 462

109 ]

Theorem 3 . 9 in which X = Y * and I ' = Y , was

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

gave ...

109 ]

**proved**3 . 9 after establishing Lemma 3 . 10 by induction . The case ofTheorem 3 . 9 in which X = Y * and I ' = Y , was

**proved**in the separable case byBanach [ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p . 256 ) . Michael [ 1 ]

gave ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

### Other editions - View all

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