## Linear Operators, Part 2 |

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Page 1449

for ao

then oe ( T ) is void . ( d ) If a ( t ) + -0 , it is monotone decreasing for

large t , if Si ce n - 3 ( acere 9 ( 0 ) ' 19 ( t ) 3 ( g ( t ) ) 19 ( t ) | 5/2 dt < đo for a ...

for ao

**sufficiently**large , and if ro L 19 ( 0 ) 1 = Ydt < 0 do for Q**sufficiently**large ,then oe ( T ) is void . ( d ) If a ( t ) + -0 , it is monotone decreasing for

**sufficiently**large t , if Si ce n - 3 ( acere 9 ( 0 ) ' 19 ( t ) 3 ( g ( t ) ) 19 ( t ) | 5/2 dt < đo for a ...

Page 1450

q ' ( t ) ( g ( t ) ' ) 2 - 1 4 dt < 9 ( t ) 3/2 ) 0 19 ( t ) / 5 / 2 for

if bo $ * iq ( t ) - % dt < 0 for

-00 as t → 0 , 9 ( t ) is monotone decreasing for

...

q ' ( t ) ( g ( t ) ' ) 2 - 1 4 dt < 9 ( t ) 3/2 ) 0 19 ( t ) / 5 / 2 for

**sufficiently**small bo , andif bo $ * iq ( t ) - % dt < 0 for

**sufficiently**small bo , then o . ( T ) is void . ( d ) If g ( t )-00 as t → 0 , 9 ( t ) is monotone decreasing for

**sufficiently**small t , • ნი con los...

Page 1760

... Sk is bounded and of norm at most Mk . We shall show that ( vii ) for each k 20 ,

and for each

dense in K ( C ) . Suppose that ( v ) is false , but that ( vii ) has been established .

... Sk is bounded and of norm at most Mk . We shall show that ( vii ) for each k 20 ,

and for each

**sufficiently**small positive a Sak ) , the mapping 1-9Sx has a rangedense in K ( C ) . Suppose that ( v ) is false , but that ( vii ) has been established .

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero