## Linear Operators: General theory |

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Page 136

There is a uniquely

o - field containing a given family of sets . Proof . There is at least one field ,

namely the field of all subsets of S , which contains a given family t . The

intersection ...

There is a uniquely

**determined**smallest field and a uniquely**determined**smallesto - field containing a given family of sets . Proof . There is at least one field ,

namely the field of all subsets of S , which contains a given family t . The

intersection ...

Page 455

Let G = U_ Yn ; then f is

subset of X * , there exists a denumerable subset G , of X * such that each feF is

can be ...

Let G = U_ Yn ; then f is

**determined**by G. It follows that if F is a denumerablesubset of X * , there exists a denumerable subset G , of X * such that each feF is

**determined**by GF We can even assert that each continuous linear functional fcan be ...

Page 657

Since y is uniquely

the equation y = $ 1 ( x ) . The flow do is assumed to have the property that ( i ) $ (

$ s ( x ) ) = $ e + s ( x ) , for all points x in phase space and for all times s and t .

Since y is uniquely

**determined**by x and t , a function de on S to S is defined bythe equation y = $ 1 ( x ) . The flow do is assumed to have the property that ( i ) $ (

$ s ( x ) ) = $ e + s ( x ) , for all points x in phase space and for all times s and t .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

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 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