## Linear Operators, Part 2 |

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Page 1092

Note that if T has finite - dimensional

Note that if T has finite - dimensional

**range**, T = ET , where E is the orthogonal projection on the**range**of T. Thus T * = T * E * , so that T * also has ...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

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 ...Page 1397

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

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

**range**R ( T ) of T is closed .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

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