## Linear Operators: General theory |

### From inside the book

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Page v

Preface In the two parts of Linear Operators we endeavor to give a

comprehensive survey of the general

survey of the application of this general

classical analysis.

Preface In the two parts of Linear Operators we endeavor to give a

comprehensive survey of the general

**theory**of linear operations, together with asurvey of the application of this general

**theory**to the diverse fields of moreclassical analysis.

Page vi

of arbitrary operators into the first part; all material relating to the

completely reducible operators into the second part. Of course, we have

occasionally ...

**theory**of spaces and operators, and all material pertaining to the spectral**theory**of arbitrary operators into the first part; all material relating to the

**theory**ofcompletely reducible operators into the second part. Of course, we have

occasionally ...

Page viii

close to Chapter XIII, and also discusses some points of the

Chapter XIX. Surveying in netrospect the

twenty chapters, it seems to the authors that the general

chapters, ...

close to Chapter XIII, and also discusses some points of the

**theory**given inChapter XIX. Surveying in netrospect the

**theories**presented in the followingtwenty chapters, it seems to the authors that the general

**theory**of the first sevenchapters, ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 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

a-finite Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space valued function vector space weak topology weakly compact weakly sequentially compact zero