## Linear Operators: General theory |

### From inside the book

Results 1-3 of 57

Page v

Thus , a very elaborate analysis (

self - adjoint differential operators is presented , while on the other hand the

theory of locally convex spaces is treated (

connection ...

Thus , a very elaborate analysis (

**Chapter**XIII ) of the spectral theory of ordinaryself - adjoint differential operators is presented , while on the other hand the

theory of locally convex spaces is treated (

**Chapter**V ) rather briefly in itsconnection ...

Page vii

Many of the

have a dual purpose . On the ... to the original and subsequent papers in which

the principal results of the

literature .

Many of the

**chapters**end with sections entitled “ Notes and Remarks ” , whichhave a dual purpose . On the ... to the original and subsequent papers in which

the principal results of the

**chapter**in question have been discussed in theliterature .

Page viii

close to

twenty

close to

**Chapter**XIII , and also discusses some points of the theory given in**Chapter**XIX . Surveying in netrospect the theories presented in the followingtwenty

**chapters**, it seems to the authors that the general theory of the first seven**chapters**...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

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