## Linear Operators: Spectral theory |

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Page 1452

It is

It is

**evident**from Definition XII.5.1 that if T , is bounded below , T , must also be bounded below . Conversely , let T be bounded below . Suppose that the lemma is false , so that T , is not bounded below . We shall show by induction ...Page 1631

1 It is

1 It is

**evident**that T is linear , and equally**evident**that T is closed . Hence , by the closed graph theorem ( II.2.4 ) , T is continuous . Hence given any a > 0 and any k , there is an integer l and a d > 0 such that ulk , T [ go , .Page 1662

However , an

However , an

**evident**consequence of Lemma 12 , as generalized to D , ( 1 ) , which will be of importance to us in subsequent discussions , is stated in the following lemma . TT 33 LEMMA . Let I be an open subset of the interior of C ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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