## Linear Operators: General theory |

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Page 387

A detailed proof was

1 < p < 0o , was demonstrated by F . Riesz [ 2 ; p . 475 ] . In the case of a finite

measure space the theorem was established by Nikodým [ 9 ; p . 132 ] and later

by ...

A detailed proof was

**given**by Fréchet [ 5 ; III . p . 441 ] . The theorem for L [ 0 , 1 ] ,1 < p < 0o , was demonstrated by F . Riesz [ 2 ; p . 475 ] . In the case of a finite

measure space the theorem was established by Nikodým [ 9 ; p . 132 ] and later

by ...

Page 392

tion with respect to a vector valued measure which is presented here is the one

employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both

...

tion with respect to a vector valued measure which is presented here is the one

**given**in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has beenemployed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both

...

Page 729

proofs , valid in uniformly convex spaces , were

Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for

a contraction in Hilbert space is also a fixed point for its adjoint , was

proofs , valid in uniformly convex spaces , were

**given**by G . Birkhoff [ 7 ] and F .Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for

a contraction in Hilbert space is also a fixed point for its adjoint , was

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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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