## Linear Operators: General theory |

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Page 224

Functions of a

especially in Chapter VII , we shall use extensions of certain well - known results

in the theory of analytic functions of a

functions ...

Functions of a

**Complex**Variable In some of the chapters to follow , andespecially in Chapter VII , we shall use extensions of certain well - known results

in the theory of analytic functions of a

**complex**variable to the case where thefunctions ...

Page 238

With the one exception of Hilbert space, each of them will consist of real or

and multiplication are understood to be defined in the natural way, i.e., by the

equations ...

With the one exception of Hilbert space, each of them will consist of real or

**complex**valued functions /, g defined on a specified domain S. Here, additionand multiplication are understood to be defined in the natural way, i.e., by the

equations ...

Page 238

With the one exception of Hilbert space , each of them will consist of real or

and multiplication are understood to be defined in the natural way , i.e. , by the ...

With the one exception of Hilbert space , each of them will consist of real or

**complex**valued functions f , g defined on a specified domain S. Here , additionand multiplication are understood to be defined in the natural way , i.e. , by the ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero