## Linear Operators: Spectral operators |

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Page 1953

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

COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is the only bounded linear

operator for which either AT = ( or TA = 0 .

...

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

COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is the only bounded linear

operator for which either AT = ( or TA = 0 .

**PROOF**. If either AT = 0 or TA = 0 then...

Page 2137

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each lemma in the

which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are

vectors in ...

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each lemma in the

**proof**ofwhich it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are

vectors in ...

Page 2218

algebra A generated by the projections in its resolution of the identity , it suffices

to show that every operator in A is a spectral operator of scalar type . This follows

...

**PROOF**. Since a spectral operator of scalar type is clearly in the weakly closedalgebra A generated by the projections in its resolution of the identity , it suffices

to show that every operator in A is a spectral operator of scalar type . This follows

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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