## Linear Operators: Spectral theory |

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Page 1092

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator

may be approximated in norm by a sequence of operators Tn with

finitedimensional

T has finite ...

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator

may be approximated in norm by a sequence of operators Tn with

finitedimensional

**range**, it is enough to prove the lemma in the special case thatT has finite ...

Page 1134

Then , retracing the steps of the above argument , we can conclude that ( I –

EWTE = 0 for each 2 in C . Hence T leaves the

invariant , and the set F of projections En , de C ; subdiagonalizes T . To prove

the second ...

Then , retracing the steps of the above argument , we can conclude that ( I –

EWTE = 0 for each 2 in C . Hence T leaves the

**range**of each projection E ,invariant , and the set F of projections En , de C ; subdiagonalizes T . To prove

the second ...

Page 1397

This readily yields a contradiction as follows : the assumption that 0 0 ( T ) implies

that the

seen to be symmetric — obtained by restricting T * to D ( T ) + N . Then the

R ...

This readily yields a contradiction as follows : the assumption that 0 0 ( T ) implies

that the

**range**R ( T ) of T is closed . Let Tį be the extension — which is easilyseen to be symmetric — obtained by restricting T * to D ( T ) + N . Then the

**range**R ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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