## Linear Operators: General theory |

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Page v

Physier Library QA 251 Dale Vol Preface In the two parts of Linear Operators we

endeavor to give a com. prehensive survey of the general

operations , together with a survey of the application of this general

...

Physier Library QA 251 Dale Vol Preface In the two parts of Linear Operators we

endeavor to give a com. prehensive survey of the general

**theory**of linearoperations , together with a survey of the application of this general

**theory**to the...

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

...

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 seven...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero