## Linear Operators: General theory |

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Page 2

This

x u a ) . Moreover , there are identities , known as the rules of De Morgan , which

relate the operations of complementation , taking unions , and taking

intersections .

This

**means**that the following distributive laws hold : xa = ( xa ) , xu ( na ) = n (x u a ) . Moreover , there are identities , known as the rules of De Morgan , which

relate the operations of complementation , taking unions , and taking

intersections .

Page 381

Glicksberg [ 1 ] showed that if S is completely regular , then every non - negative

functional on C ( S ) may be represented by

measure if and only if any one of the following conditions hold : ( 1 ) In E C ...

Glicksberg [ 1 ] showed that if S is completely regular , then every non - negative

functional on C ( S ) may be represented by

**means**of a countably additivemeasure if and only if any one of the following conditions hold : ( 1 ) In E C ...

Page 476

These topologies are by no

Other topologies in B ( X , Y ) can be introduced in such a way that the

convergence of a generalized sequence { Ta } to a limit T

following : ( i ) ...

These topologies are by no

**means**the only interesting topologies of B ( X , Y ) .Other topologies in B ( X , Y ) can be introduced in such a way that the

convergence of a generalized sequence { Ta } to a limit T

**means**any one of thefollowing : ( i ) ...

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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