## Linear Operators: Spectral operators |

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Page 2056

Chrysippus introduced the notion of " condestinate ”

to recover only if he calls a physician . ... and many philosophers between these

two , rejected Plato ' s reasoning on the grounds that it contradicts the

Chrysippus introduced the notion of " condestinate ”

**facts**which allows the manto recover only if he calls a physician . ... and many philosophers between these

two , rejected Plato ' s reasoning on the grounds that it contradicts the

**fact**that ...Page 2080

Show that o ( L ) = { a112131 , in

a111 = 1 } . Calculate the maximal extension of R ( A ; L ) xm , where X = ( 8mm ) .

39 Let X be the B - space of all bounded complex sequences x = { Én ! - 00 < n <

+ ...

Show that o ( L ) = { a112131 , in

**fact**, Op ( L ) = { a1111 < 1 } and oc ( L ) = {a111 = 1 } . Calculate the maximal extension of R ( A ; L ) xm , where X = ( 8mm ) .

39 Let X be the B - space of all bounded complex sequences x = { Én ! - 00 < n <

+ ...

Page 2262

T ) = 0 , so that T ( h ) = T . Using the above

( T ) and has a double zero at d = 0 and we let fi ( a ) = ( 1 - vö ? ) f ( a ) , then ( T –

vő ' I ) ( T ) = f ( 1 ) = T ( f ) = ( T – vs I ) T ( f ) . Thus E . ( f ( T ) – T ( $ ) ) = 0 .

T ) = 0 , so that T ( h ) = T . Using the above

**facts**, it follows that if f is analytic on o( T ) and has a double zero at d = 0 and we let fi ( a ) = ( 1 - vö ? ) f ( a ) , then ( T –

vő ' I ) ( T ) = f ( 1 ) = T ( f ) = ( T – vs I ) T ( f ) . Thus E . ( f ( T ) – T ( $ ) ) = 0 .

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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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