## Linear Operators: General theory |

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Page 477

strong , and the weak

uniform

the strong

...

strong , and the weak

**operator**topologies in B ( X , Y ) . It is evident that theuniform

**operator**topology is stronger than the strong**operator**topology , and thatthe strong

**operator**topology is stronger than the weak**operator**topology . With its...

Page 511

Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the

product Pxex Yz , where Yz = y , under the mapping T → Prex Tx . Show that the

strong topology of

Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the

product Pxex Yz , where Yz = y , under the mapping T → Prex Tx . Show that the

strong topology of

**operators**in B ( X , Y ) is identical with the usual product ...Page 838

12 . 1 ( 41 ) Borel field of sets , definition , III . 5 . 10 ( 137 ) Borel measure ( or

Borel - Lebesgue measure ) , construction of , ( 139 ) III . 13 . 8 ( 223 ) Borel -

Stieltjes measure , ( 142 ) Bound , of an

ordered set ...

12 . 1 ( 41 ) Borel field of sets , definition , III . 5 . 10 ( 137 ) Borel measure ( or

Borel - Lebesgue measure ) , construction of , ( 139 ) III . 13 . 8 ( 223 ) Borel -

Stieltjes measure , ( 142 ) Bound , of an

**operator**, II . 3 . 5 ( 60 ) in a partiallyordered set ...

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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