## Linear Operators: General theory |

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Results 1-3 of 76

Page 373

This generalizes and abstracts a result

, 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 L [ 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 463

124 ] also

with that of closure in the X topology of X * . Alaoglu ( 1 ; p . 256 ) and Kakutani ( 2

; p . 170 ] independently established the equivalence of these types of closure ...

124 ] also

**proved**that in the case of a separable space these notions coincidewith that of closure in the X topology of X * . Alaoglu ( 1 ; p . 256 ) and Kakutani ( 2

; p . 170 ] independently established the equivalence of these types of closure ...

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### Contents

Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 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 |

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