## Linear Operators: General theory |

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Page 169

8 Show that S can be the union of an increasing sequence of null sets even if u is

not identically

subset of X , and if f - 1 ( G ) is in for each open subset G of X , then f is totally u ...

8 Show that S can be the union of an increasing sequence of null sets even if u is

not identically

**zero**. 9 Show that if f is defined on S and has values in a compactsubset of X , and if f - 1 ( G ) is in for each open subset G of X , then f is totally u ...

Page 204

Since u ( Fm ) = Ss , In ( San Juan ( dsq ) does not converge to

Sin ( sq ) si it follows from the dominated convergence theorem ( 6 . 16 ) that

there is a point se , in Sq , for which In ( $ C , ) is defined for all n and for which

the ...

Since u ( Fm ) = Ss , In ( San Juan ( dsq ) does not converge to

**zero**and since 0Sin ( sq ) si it follows from the dominated convergence theorem ( 6 . 16 ) that

there is a point se , in Sq , for which In ( $ C , ) is defined for all n and for which

the ...

Page 452

If A is a subset of X , and p is in A , then there exists a non -

linear functional tangent to A at p if and only if the cone B with vertex p generated

by A is not dense in X . Proof . If q¢K , then , by 2 . 12 we can find a functional f

and a ...

If A is a subset of X , and p is in A , then there exists a non -

**zero**continuouslinear functional tangent to A at p if and only if the cone B with vertex p generated

by A is not dense in X . Proof . If q¢K , then , by 2 . 12 we can find a functional f

and a ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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