## Linear Operators: General theory |

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Page 243

The norm in H is | x | = ( x , x ) 1 / 2 . Remark .

a set of abstract axioms . It is noteworthy that some of the concrete spaces

defined above satisfy these axioms , and hence are special cases of abstract

Hilbert ...

The norm in H is | x | = ( x , x ) 1 / 2 . Remark .

**Hilbert space**has been defined bya set of abstract axioms . It is noteworthy that some of the concrete spaces

defined above satisfy these axioms , and hence are special cases of abstract

Hilbert ...

Page 256

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . ,

Xn are

explicit ...

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . ,

Xn are

**Hilbert spaces**then it will always be understood , sometimes withoutexplicit ...

Page 851

4 ( 59 ) discussion of , ( 82 - 83 ) in F - spaces , II . 1 . ... 72 ( 350 ) , ( 561 ) ideals

of , ( 552 – 553 ) , ( 611 ) identity , ( 37 ) limits of , in B - spaces , II . 3 . ... 17 ( 72 )

remarks on , ( 93 ) Orthogonal elements and manifolds in

4 ( 59 ) discussion of , ( 82 - 83 ) in F - spaces , II . 1 . ... 72 ( 350 ) , ( 561 ) ideals

of , ( 552 – 553 ) , ( 611 ) identity , ( 37 ) limits of , in B - spaces , II . 3 . ... 17 ( 72 )

remarks on , ( 93 ) Orthogonal elements and manifolds in

**Hilbert space**, IV . 4 .### What people are saying - Write a review

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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 |

### Common terms and phrases

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