## Linear Operators: General theory |

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Page 838

space of ,

. 17 ( 72 ) Arzelą theorem , on continuity of limit function , IV . 6 . 11 ( 268 )

remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of

continuous ...

space of ,

**definition**, IV . 2 . 24 ( 242 ) properties , IV . 15 Annihilator of a set , II . 4. 17 ( 72 ) Arzelą theorem , on continuity of limit function , IV . 6 . 11 ( 268 )

remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of

continuous ...

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Closed orthonormal system ,

set ,

1 ( 70 ) Closed unit sphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in , 1 .

Closed orthonormal system ,

**definition**, IV . 14 . 1 ( 357 ) study of , IV . 14 Closedset ,

**definition**, 1 . 4 . 3 ( 10 ) properties , 1 . 4 . 4 - 5 ( 10 ) Closed sphere , 11 . 4 .1 ( 70 ) Closed unit sphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in , 1 .

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11 ( 100 - 101 ) Essential singularity ,

17 ( 23 ) ...

11 ( 100 - 101 ) Essential singularity ,

**definition**, ( 229 ) Essential supremum ,**definition**, III . 1 . 11 ( 100 - 101 ) ... 3 Extended real and complex numbers ,**definitions**, ( 3 ) topology of , ( 11 ) Extension of a function , by continuity , 1 . 6 .17 ( 23 ) ...

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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