## Linear Operators, Part 1 |

### From inside the book

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Page 3

The restriction of a function f to a subset A of its

f | A . If f : A + B , and for each bef ( A ) there is only one a € A with f ( a ) = b , f is

said to have an inverse or to be one - to - one . The inverse function has

...

The restriction of a function f to a subset A of its

**domain**is sometimes denoted byf | A . If f : A + B , and for each bef ( A ) there is only one a € A with f ( a ) = b , f is

said to have an inverse or to be one - to - one . The inverse function has

**domain**f...

Page 230

Let f be an analytic function defined on a connected

plane and having its values in a complex B - space X. Then f ( x ) does not have

its maximum at any point of the

Let f be an analytic function defined on a connected

**domain**D in the complexplane and having its values in a complex B - space X. Then f ( x ) does not have

its maximum at any point of the

**domain**D , unless \ f ( z ) | is identically constant .Page 539

145–152 ] although his proofs are different . For additional results of this nature

the reader may consult Hausdorff [ 3 ] and Dieudonné [ 3 ] . Representation of

operators in C. The representation of the general operator with

range in ...

145–152 ] although his proofs are different . For additional results of this nature

the reader may consult Hausdorff [ 3 ] and Dieudonné [ 3 ] . Representation of

operators in C. The representation of the general operator with

**domain**andrange in ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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