## Linear Operators: Spectral theory |

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Results 1-3 of 92

Page 898

If E is the resolution of the

of complex numbers , then EDT = TE ( 8 ) , 0 ( T8 ) ÇJ , where To is the restriction

of T to E ( 8 ) Ý . Proof . The first statement follows from Theorem 1 ( ii ) . Now for ...

If E is the resolution of the

**identity**for the normal operator T and if d is a Borel setof complex numbers , then EDT = TE ( 8 ) , 0 ( T8 ) ÇJ , where To is the restriction

of T to E ( 8 ) Ý . Proof . The first statement follows from Theorem 1 ( ii ) . Now for ...

Page 920

Under this assumption it will be shown that there is an ordered representation of

H onto , L , lên , ū ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ể be the resolutions of the

Under this assumption it will be shown that there is an ordered representation of

H onto , L , lên , ū ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ể be the resolutions of the

**identity**for T and T respectively .Page 1717

By induction on Jil , we can readily show that a formal

= C ( x ) 201 202 + 3 CJ , 1 , ay ( x ) ... Making use of

may evidently proceed to prove by induction on the order of t that t may be ...

By induction on Jil , we can readily show that a formal

**identity**( 1 ) 2010 ( x ) 2J3= C ( x ) 201 202 + 3 CJ , 1 , ay ( x ) ... Making use of

**identities**of the type ( 1 ) , wemay evidently proceed to prove by induction on the order of t that t may be ...

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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