## Linear Operators, Part 1 |

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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...

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2n ) for every point 212 ... , En in U , and if every point in V can be connected to a

point of U by a continuous curve lying in V. If f admits no analytic continuations , U

is said to be the natural

2n ) for every point 212 ... , En in U , and if every point in V can be connected to a

point of U by a continuous curve lying in V. If f admits no analytic continuations , U

is said to be the natural

**domain**of existence of f . The well known maximum ...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

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### 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