## Linear Operators: General theory |

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Page 262

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theorem is a converse to this statement . 2 THEOREM . Is S is normal , there is an

isometric isomorphism between C * ( S ) and rba ( S ) such that corresponding ...

...

**clear**that the integral is a continuous linear functional on C ( S ) . The followingtheorem is a converse to this statement . 2 THEOREM . Is S is normal , there is an

isometric isomorphism between C * ( S ) and rba ( S ) such that corresponding ...

Page 282

It is

function f is said to be almost periodic if it is continuous and if for every e > 0 there

is an L = L ( E ) > 0 such that every interval in R of length L contains at least one ...

It is

**clear**that T ( E ) CT ( 8 ) if ε < d and that - te T ( E ) whenever te T ( $ ) . Thefunction f is said to be almost periodic if it is continuous and if for every e > 0 there

is an L = L ( E ) > 0 such that every interval in R of length L contains at least one ...

Page 292

Let £ be the family of all sets E in E for which lim un ( EF ) exists for each F € Ej ,

and let Ez be the family of all sets E 0700 in E , for which EF € £ , for each Fe Eg .

It is

...

Let £ be the family of all sets E in E for which lim un ( EF ) exists for each F € Ej ,

and let Ez be the family of all sets E 0700 in E , for which EF € £ , for each Fe Eg .

It is

**clear**that if F , and F are elements of £3 , then F F , € £g . It is also**clear**that if...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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