## Linear Operators: Spectral operators |

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Page 2296

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

an x # 0 in S . such that Ux = 0 . Multiplying by T , however , gives TUx = x = 0 .

This contradiction proves the lemma . Q . E . D . 6 LEMMA . Let T be a

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

an x # 0 in S . such that Ux = 0 . Multiplying by T , however , gives TUx = x = 0 .

This contradiction proves the lemma . Q . E . D . 6 LEMMA . Let T be a

**discrete**...Page 2356

Let 0 sv < 1 , and put My = max lul " la - ul - 1 . NEVI . NEO ( T ) Let 10 € ( T ) , and

let P be an operator such that P ( T - 101 ) - ° is bounded . Then ( a ) if we →0 , T

+ P is

...

Let 0 sv < 1 , and put My = max lul " la - ul - 1 . NEVI . NEO ( T ) Let 10 € ( T ) , and

let P be an operator such that P ( T - 101 ) - ° is bounded . Then ( a ) if we →0 , T

+ P is

**discrete**and S . ( T + P ) = 0 ; ( b ) if lim supira Mi SKS OO , there exists a S...

Page 2362

( a ) if di → 00 , then T + B is

, then there is a number ε = £ ( K , T ) > 0 such that T + B is

) = 0 whenever BI SE ; ( c ) if lim infi - adi > 0 , and B is compact , then T + B is ...

( a ) if di → 00 , then T + B is

**discrete**and S . ( T + B ) = 0 ; ( b ) if lim infi - . d , K > 0, then there is a number ε = £ ( K , T ) > 0 such that T + B is

**discrete**and S . ( T + B) = 0 whenever BI SE ; ( c ) if lim infi - adi > 0 , and B is compact , then T + B is ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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