## Linear Operators: Spectral operators |

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Page 2084

Using the fact that the difference R ( A ; A ) – R ( A ; B ) is analytic for 2 # 0 , prove

that C is a quasi - nilpotent operator and that R ( A ; A ) = R ( A ; B ) + R ( A ; C ) –

55 ( McCarthy ) Let T be a spectral operator in a

Using the fact that the difference R ( A ; A ) – R ( A ; B ) is analytic for 2 # 0 , prove

that C is a quasi - nilpotent operator and that R ( A ; A ) = R ( A ; B ) + R ( A ; C ) –

55 ( McCarthy ) Let T be a spectral operator in a

**complex**B - space X which ...Page 2171

Exercises Some of the exercises will use the following notation . The symbol T is

a bounded linear operator on a

[ x ] will be used for the closed linear manifold determined by all the vectors R ( £

...

Exercises Some of the exercises will use the following notation . The symbol T is

a bounded linear operator on a

**complex**B - space X . For each x in X the symbol[ x ] will be used for the closed linear manifold determined by all the vectors R ( £

...

Page 2188

Let E be a spectral measure in the

countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel

measurable function defined on the

...

Let E be a spectral measure in the

**complex**B - space X which is defined andcountably additive on a o - field of subsets of a set 1 and let g be a bounded Borel

measurable function defined on the

**complex**plane . Then $ 9 ( f ( n ) ) E ( da ) = g...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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