## Linear Operators, Volume 2 |

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Page 898

If E is the resolution of the

If E is the resolution of the

**identity**for the normal operator T and if d is a Borel set of complex numbers , then E ( ) T = TE ( 8 ) , o ( T8 ) C3 , where To is the restriction of T to E ( OH . Proof . The first statement follows from ...Page 920

Let E and Ể be the resolutions of the

Let E and Ể be the resolutions of the

**identity**for T and † respectively . From Corollary 2.7 it is seen that Ể = VEV - 1 and hence that F ( † ) = VF ( T ) V - 1 for every bounded Borel function F. The mapping W = Ū V of H onto En - 1 ...Page 1717

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

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

**identity**( 1 ) J01C ( x ) 213 = C ( x ) 21212 + Σ C1,1 ... Making use of**identities**of the type ( 1 ) , we may evidently proceed to prove by induction on the order of 1 that may be ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 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 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero