## Linear Operators: General theory |

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Page 177

n - 00 0 - 00 may be

be represented as the difference of its positive and negative variations ( 4 . 11 )

and so we may also assume that a is positive . Let , then , { En } be a sequence ...

n - 00 0 - 00 may be

**assumed**that 2 is real valued . A real valued set function canbe represented as the difference of its positive and negative variations ( 4 . 11 )

and so we may also assume that a is positive . Let , then , { En } be a sequence ...

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

has ...

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 HỆ = Hj . Then H is continuous andhas ...

Page 657

The problem may be formulated in abstract terms as follows : The momentary

state of a mechanical system is described by specifying a point in a " phase

space ” S. The mechanical system is

The problem may be formulated in abstract terms as follows : The momentary

state of a mechanical system is described by specifying a point in a " phase

space ” S. The mechanical system is

**assumed**to be governed by the classical ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

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### 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

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero