## 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 - E )

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

, 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 - E )

TE , = 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 € 0e ( T )

implies that the

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

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

implies that the

**range**R ( T ) of T is closed . Let T , be the extension – which iseasily seen to be symmetric obtained by restricting T * to D ( T ) + N . Then the

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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