## Linear Operators, Part 1 |

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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

**given**by ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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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 obtained 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