## Linear Operators, Part 1 |

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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 728

treatment was

generator of a group , it is possible to extend the class of functions to include

polynomials and other functions with similar growth conditions . The treatment in

...

treatment was

**given**by Phillips ( 5 ) . Bade ( 1 ) showed that for the infinitesimalgenerator of a group , it is possible to extend the class of functions to include

polynomials and other functions with similar growth conditions . The treatment in

...

Page 729

bons et Shir : of P. Lite er r beid r3.1 Telt proofs , valid in uniformly convex spaces

, were

the interesting fact that a fixed point for a contraction in Hilbert space is also a ...

bons et Shir : of P. Lite er r beid r3.1 Telt proofs , valid in uniformly convex spaces

, were

**given**by G. Birkhoff [ 7 ] and F. Riesz ( 16 , 18 ] . Another proof , based onthe interesting fact that a fixed point for a contraction in Hilbert space is also a ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero