## Linear Operators: General theory |

### From inside the book

Results 1-3 of 67

Page 464

( 3 ) For every f e T ' , sup.xek Rf ( x ) < 0o ; moreover , each linear functional Ø on

l ' which

= f ( xo ) , fel for some x , € K. ( 4 ) If K. , & < 0 , 0 a limit ordinal , is a monotone ...

( 3 ) For every f e T ' , sup.xek Rf ( x ) < 0o ; moreover , each linear functional Ø on

l ' which

**satisfies**inf Rf ( x ) < RÓ ( ) sup Rf ( x ) , fel → XeK XEK also**satisfies**( 1 )= f ( xo ) , fel for some x , € K. ( 4 ) If K. , & < 0 , 0 a limit ordinal , is a monotone ...

Page 498

ΕΕΣ ΕεΣ Conversely , if æ * ( - ) on to X *

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

weakly compact if and only if x * ( - ) is countably additive on E in the strong

topology of X * .

ΕΕΣ ΕεΣ Conversely , if æ * ( - ) on to X *

**satisfies**( i ) then ( ii ) defines anoperator T on X to L ( S , E , u ) whose norm

**satisfies**( iii ) . Furthermore T isweakly compact if and only if x * ( - ) is countably additive on E in the strong

topology of X * .

Page 557

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

, still

where Bi min ( ai , v ( 2 ; ) ) ,

Consequently , the product R , of all the factors ( 2–2 ; ) i 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 ) ,where Bi min ( ai , v ( 2 ; ) ) ,

**satisfies**R2 ( T ) . = 0. Since any polynomial P ...### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero