## Linear Operators: General theory |

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Page 177

may be

may be

**assumed**that 2 is real valued . ... as the difference of its positive and negative variations ( 4.11 ) and so we may also**assume**that 1 is positive .Page 657

The flow do is

The flow do is

**assumed**to have the property that ( i ) f ( $ ( x ) ) $ ++ s ( x ) , for all points æ in phase space and for all times s and t .Page 675

We may and shall

We may and shall

**assume**that | 2 0. Let a ' be the complement of the set a = { s \ / ( s ) 2 1 } . Since f € L , it follows that ula ) < oo and thus f is ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero