## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

### From inside the book

Results 1-3 of 40

Page 2327

it follows that there exist at least two linearly

equation to = do q such that Bi ( 91 ) = B : ( 92 ) = 0 , i = 1 , . . . , k . Then 21 may

be represented uniquely as 91 = } = 1 C1 ; 0 ; ( u ( a ) ) and , similarly , P2 = ) = 1 ...

it follows that there exist at least two linearly

**independent**solutions P1 , 92 of theequation to = do q such that Bi ( 91 ) = B : ( 92 ) = 0 , i = 1 , . . . , k . Then 21 may

be represented uniquely as 91 = } = 1 C1 ; 0 ; ( u ( a ) ) and , similarly , P2 = ) = 1 ...

Page 2394

On the other hand , since these two solutions are linearly

have a linear relation o2 = aới + boy . It is clear from Lemma 1 that such a linear

combination can only have the indicated asymptotic form if a = 1 , b = c ( u ( a ) ) .

On the other hand , since these two solutions are linearly

**independent**, we musthave a linear relation o2 = aới + boy . It is clear from Lemma 1 that such a linear

combination can only have the indicated asymptotic form if a = 1 , b = c ( u ( a ) ) .

Page 2441

This shows that there exists a finite absolute constant c ' such that 1 ( a ) c ' ( 1 +

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite

constant M "

This shows that there exists a finite absolute constant c ' such that 1 ( a ) c ' ( 1 +

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite

constant M "

**independent**of ε such that ( 43 ) 17 6 . + younger og levererar o ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero