## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 89

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 ( S ) T = TE ( 8 ) , 8 ( o ( T3 ) CJ , where T , is the restriction of T to E ( ) . PROOF . The first statement follows ...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 Ě = VEV - 1 and hence that F ( T ) = VF ( T ) V - 1 for every bounded Borel function F. The mapping W = Ũy of 5 onto - Lelên ...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 ) 201 C ( x ) 212 = C ( x ) DJ1242 + Σ C1,1 ... Making use of**identities**of the type ( 1 ) , we may evidently proceed to prove by induction on the order of t that t ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

46 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad 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 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