## Linear Operators: Spectral theory |

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Page 1080

34 ( Bendixon ) Let A be as in Exercise 25 , and suppose also that the matrix

absolute values of the matrix

Exercise ...

34 ( Bendixon ) Let A be as in Exercise 25 , and suppose also that the matrix

**elements**of A are real . Let C = ( A – A * ) , and let g be the maximum of theabsolute values of the matrix

**elements**of C . Then In ( n - 1 ) 1 Ill Sg 2 ( Hint : UseExercise ...

Page 1339

An

set of all equivalence classes of

functions will be denoted by L2 ( { Mis } ) . We observe that by Lemma 7 , the ...

An

**element**F of L ( { uis } ) will be said to be a { wiss - null function if ( F \ = 0 . Theset of all equivalence classes of

**elements**of Ly ( { uis } ) modulo { lij } - nullfunctions will be denoted by L2 ( { Mis } ) . We observe that by Lemma 7 , the ...

Page 1436

Let { gn } be a bounded sequence of

converges . Find a subsequence { & n , } = { hi } such that x * ( hi ) converges for

each j , 1 si sk . Then hi = h ; - * - * * ( hi ) ; is in D , and Tħ ; = Thị . Thus { ħi }

converges ...

Let { gn } be a bounded sequence of

**elements**of D ( T ) such that { Tgn }converges . Find a subsequence { & n , } = { hi } such that x * ( hi ) converges for

each j , 1 si sk . Then hi = h ; - * - * * ( hi ) ; is in D , and Tħ ; = Thị . Thus { ħi }

converges ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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