## Linear Operators: Spectral theory |

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Page 898

If we put E ( 8 ) = 0 when d n ( T ) is void , then

from Theorem 1 and

defined spectral measure associated , in

is ...

If we put E ( 8 ) = 0 when d n ( T ) is void , then

**Corollary**4 follows immediatelyfrom Theorem 1 and

**Corollary**IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquelydefined spectral measure associated , in

**Corollary**4 , with the normal operator Tis ...

Page 1142

14 . Q . E . D . In what follows , we will use the symbols p and n to denote the

continuous extension to the classes Co of operators of the mappings p and n of

the previous lemma . We will also write t ( p + n ) 2 . We note the following

14 . Q . E . D . In what follows , we will use the symbols p and n to denote the

continuous extension to the classes Co of operators of the mappings p and n of

the previous lemma . We will also write t ( p + n ) 2 . We note the following

**corollary**.Page 1301

Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo

satisfies an equation of order 2n , v , must be identically zero . This contradiction

completes the proof . Q . E . D . 23

Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo

satisfies an equation of order 2n , v , must be identically zero . This contradiction

completes the proof . Q . E . D . 23

**COROLLARY**. Let t be a formal differential ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero