## Linear Operators, Part 1 |

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Page 243

some of the concrete spaces defined above satisfy these axioms , and hence are

special cases of abstract

**Hilbert space**has been defined by a set of abstract axioms . It is noteworthy thatsome of the concrete spaces defined above satisfy these axioms , and hence are

special cases of abstract

**Hilbert space**. Thus , for instance , the n - dimensional ...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 | 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