## Linear Operators: General theory |

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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 | 34 |

Copyright | |

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### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero