## Linear Operators, Part 1 |

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Page 177

Nelson Dunford, Jacob T. Schwartz. 1 - 00 n - may be

valued . A real valued set function can be represented as the difference of its

positive and negative variations ( 4 . 11 ) and so we may also assume that a is

positive .

Nelson Dunford, Jacob T. Schwartz. 1 - 00 n - may be

**assumed**that 2 is realvalued . A real valued set function can be represented as the difference of its

positive and negative variations ( 4 . 11 ) and so we may also assume that a is

positive .

Page 278

Let H be an algebraic homomorphism of C ( S ) into C ( T ) , where S and T are

compact Hausdorff spaces . If the algebras C ( S ) and C ( T ) are over the field of

complex numbers , it is also

...

Let H be an algebraic homomorphism of C ( S ) into C ( T ) , where S and T are

compact Hausdorff spaces . If the algebras C ( S ) and C ( T ) are over the field of

complex numbers , it is also

**assumed**that Hf = Hj . Then H is continuous and has...

Page 650

We have

independent of n . In the first paragraph of the proof of Lemma 7 it was seen that

R ( 2 , A ) is uniformly bounded in any half plane R ( 2 ) > wte and in any half

plane R ...

We have

**assumed**that Pn ( 2 ) / ( 2 ) SM in a strip R ( 2 ) < w + ɛ , where ɛ isindependent of n . In the first paragraph of the proof of Lemma 7 it was seen that

R ( 2 , A ) is uniformly bounded in any half plane R ( 2 ) > wte and in any half

plane R ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 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

Akad 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 isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric 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