## Linear Operators: Spectral theory |

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Page 1452

It is

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 that for ...

It is

**evident**from Definition XII . 5 . 1 that if T , is bounded below , T , must also bebounded 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 that for ...

Page 1631

It is

closed graph theorem ( II . 2 . 4 ) , T is continuous . Hence given any e > 0 and

any k , there is an integer l and a d > 0 such that ulk , T [ go , . . . 8m - 1 ] ) <

provided ...

It is

**evident**that T is linear , and equally**evident**that T is closed . Hence , by theclosed graph theorem ( II . 2 . 4 ) , T is continuous . Hence given any e > 0 and

any k , there is an integer l and a d > 0 such that ulk , T [ go , . . . 8m - 1 ] ) <

provided ...

Page 1662

However , an

which will be of importance to us in subsequent discussions , is stated in the

following lemma . 33 LEMMA . Let I be an open subset of the interior of C , and let

F be in ...

However , an

**evident**consequence of Lemma 12 , as generalized to D . ( I ) ,which will be of importance to us in subsequent discussions , is stated in the

following lemma . 33 LEMMA . Let I be an open subset of the interior of C , and let

F be in ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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