## Linear Operators, Part 1 |

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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 zex Tx . 1 The space B ( X , Y ) is algebraically isomorphic to a

subspace of the product Prex Yu , where Ya = Y , under the mapping TẠP , Show

that the strong topology of

product ...

Exercises zex Tx . 1 The space B ( X , Y ) is algebraically isomorphic to a

subspace of the product Prex Yu , where Ya = Y , under the mapping TẠP , Show

that the strong topology of

**operators**in B ( X , Y ) is identical with the usualproduct ...

Page 540

Nelson Dunford, Jacob T. Schwartz. **

weakly complete space X. Weakly compact

treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

with ...

Nelson Dunford, Jacob T. Schwartz. **

**operator**and the**operator**mapping into aweakly complete space X. Weakly compact

**operators**from C [ 0 , 1 ] to X weretreated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

**operators**with ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero