## 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 225

These integrals may be defined as follows : Let I = { tsa St b } be an interval of the

real axis and let a be a

and of bounded variation on 1 . Then a is the parametrization of a continuous ...

These integrals may be defined as follows : Let I = { tsa St b } be an interval of the

real axis and let a be a

**complex**valued function which is defined , continuousand of bounded variation on 1 . Then a is the parametrization of a continuous ...

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

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