## Linear Operators: Spectral operators |

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Page 2094

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a

] ...

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a

**unique**resolution of the identity . Berkson and Dowson [ 1] ...

Page 2143

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 11

THEOREM ( A , B ) . Let T be a bounded linear operator in the complex B - space

X. Then there is a

E ( S ) ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 11

THEOREM ( A , B ) . Let T be a bounded linear operator in the complex B - space

X. Then there is a

**unique**spectral measure on the field S ( T ) with the propertiesE ( S ) ...

Page 2265

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Væ Ec ) = Vam ( Ec ) for each family { Ex } $ D for which V & E , E D.

Then there is a

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Væ Ec ) = Vam ( Ec ) for each family { Ex } $ D for which V & E , E D.

Then there is a

**unique**multiplicity function on B which is an extension of m on ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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