## Linear Operators: Spectral theory |

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Page 861

Nelson Dunford, Jacob T. Schwartz. given algebra X is algebraically and

topologically equivalent to the B - algebra T ( X ) . Since \ Q1 = | xel = \ Tzel = lel |

Tel it follows that the

continuous it ...

Nelson Dunford, Jacob T. Schwartz. given algebra X is algebraically and

topologically equivalent to the B - algebra T ( X ) . Since \ Q1 = | xel = \ Tzel = lel |

Tel it follows that the

**inverse**map r 1 is continuous . To see that t is alsocontinuous it ...

Page 877

Then an element y in Y has an

Consequently the spectrum of y as an element of Y is the same as its spectrum as

an element of X . PROOF . If y - 1 exists as an element of Y then , since X and Y ...

Then an element y in Y has an

**inverse**in X if and only if it has an**inverse**in y .Consequently the spectrum of y as an element of Y is the same as its spectrum as

an element of X . PROOF . If y - 1 exists as an element of Y then , since X and Y ...

Page 1311

Let T have a bounded

boundary conditions defining T is equal to the number of linearly independent

solutions of the equation tf = 0 which belong to L ( I ) . Proof . Let v be the number

of ...

Let T have a bounded

**inverse**. Then the number of linearly independentboundary conditions defining T is equal to the number of linearly independent

solutions of the equation tf = 0 which belong to L ( I ) . Proof . Let v be the number

of ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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