## Linear Operators: General theory |

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Page 421

... it can be extended to a linear functional y , on En . By IV.3.7 , y , has the form The map y n [ yı , ... , yn ] Qiyi i = 1

... it can be extended to a linear functional y , on En . By IV.3.7 , y , has the form The map y n [ yı , ... , yn ] Qiyi i = 1

**Hence**n g ( x ) = ant .Page 441

Put co ( ( qi + UnQ ) C9i + U . Then K ; is a closed , and

Put co ( ( qi + UnQ ) C9i + U . Then K ; is a closed , and

**hence**a compact , subset of co ( Q ) .**Hence**CO ( Q ) = co ( K , U ... UK ) = co ( KU .Page 485

**Hence**Yni ? 8 THEOREM . ( Gantmacher ) An operator in B ( x , y ) is weakly compact if and only if its adjoint is weakly compact . Proof .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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