## Linear Operators: General theory |

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Page 464

( 2 ) If x = , & < 0 , 0 a limit ordinal , is a transfinite sequence in K , then there is an

x , eK with lim inf R } ( xx ) f ( x ) < lim sup R } ( x ) , XEK for fel . ( 3 ) For every e l ,

suprek Rf ( x ) < 0 ; moreover , each linear functional Ø on l ' which

...

( 2 ) If x = , & < 0 , 0 a limit ordinal , is a transfinite sequence in K , then there is an

x , eK with lim inf R } ( xx ) f ( x ) < lim sup R } ( x ) , XEK for fel . ( 3 ) For every e l ,

suprek Rf ( x ) < 0 ; moreover , each linear functional Ø on l ' which

**satisfies**inf R }...

Page 498

du The norm of T

ΕεΣ Conversely , if x * ( * ) on to X *

on X to L ( S , E , u ) whose norm

...

du The norm of T

**satisfies**the relations ( iii ) sup læ * ( E ) S T < 4 sup x * ( E ) . E€ΕεΣ Conversely , if x * ( * ) on to X *

**satisfies**( i ) then ( ii ) defines an operator Ton X to L ( S , E , u ) whose norm

**satisfies**( iii ) . Furthermore T is weakly compact...

Page 557

Consequently , the product R , of all the factors ( 9 – 2 ; ) xi in R such that hi e o (

T ) , still

- 2 ; Bi , where Pi = min ( lig v ( ? ; ) ) ,

...

Consequently , the product R , of all the factors ( 9 – 2 ; ) xi in R such that hi e o (

T ) , still

**satisfies**R ( T ) = 0 . In the same way , the product R , of all the factors ( 2- 2 ; Bi , where Pi = min ( lig v ( ? ; ) ) ,

**satisfies**R , ( T ) = 0 . Since any polynomial...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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