## Linear Operators: General theory |

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Page 1

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

f | A . Iff : A + B , and for each bef ( A ) there is only one a € A with f ( a ) = 6 , 7 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 . Iff : A + B , and for each bef ( A ) there is only one a € A with f ( a ) = 6 , 7 is

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

**domain**f...

Page 3

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

f \ A . If f : A + B , and for each bej ( 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 bej ( 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

Another useful criterion for connectivity is available in the space 2 of n complex

variables , for a

lies on some simple Jordan curve contained in U . Let f be a function analytic on

a ...

Another useful criterion for connectivity is available in the space 2 of n complex

variables , for a

**domain**U in Z is connected if and only if every pair of its pointslies on some simple Jordan curve contained in U . Let f be a function analytic on

a ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 other sections not shown

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