## Linear Operators: General theory |

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Page 204

Since u ( Fn ) = Ss , tr ( $ a , Dua , ( dsa , ) does not converge to

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

there is a point sa , in S , for which In ( $ 2 . ) is defined for all n and for which the

...

Since u ( Fn ) = Ss , tr ( $ a , Dua , ( dsa , ) does not converge to

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

there is a point sa , in S , for which In ( $ 2 . ) 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 ...

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 ...

Page 595

Nelson Dunford, Jacob T. Schwartz. analogues of Theorem 1 for the weak and

strong topology , which we study next . 3 THEOREM . Let , In be in F ( T ) , and let

{ f ( T ) / n ( T ) } converge to

...

Nelson Dunford, Jacob T. Schwartz. analogues of Theorem 1 for the weak and

strong topology , which we study next . 3 THEOREM . Let , In be in F ( T ) , and let

{ f ( T ) / n ( T ) } converge to

**zero**in the weak operator topology . Suppose that { In...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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