## Linear Operators: Spectral theory |

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Page 993

Then it

. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function q has its spectral set consisting of the single point m then , for some ...

Then it

**follows**from what has just been demonstrated that ay , = Qyuv , = Qy , i . e. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function q has its spectral set consisting of the single point m then , for some ...

Page 996

1 ( d ) it

seen that olf * 9 ) Colo ) and from Lemma 12 ( c ) and the equation of = tf it

that o ( f * Q ) contains no interior point of o ( p ) . Hence olf * ) is a closed subset ...

1 ( d ) it

**follows**from the above equation that f * 9 + 0 . From Lemma 12 ( b ) it isseen that olf * 9 ) Colo ) and from Lemma 12 ( c ) and the equation of = tf it

**follows**that o ( f * Q ) contains no interior point of o ( p ) . Hence olf * ) is a closed subset ...

Page 1450

Part ( a )

12 , and ... Q . E . D . A number of additional criteria of this sort for the second

order operator 2 - ( ) * + 960 )

6 .

Part ( a )

**follows**immediately from Theorem 9 . Part ( b )**follows**from Corollary 6 .12 , and ... Q . E . D . A number of additional criteria of this sort for the second

order operator 2 - ( ) * + 960 )

**follow**from the corresponding theorems of Section6 .

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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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