## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 79

Page 1247

Hence , by Theorem X.4.2 . , o ( T ) C ( 0 , 0 ) . Thus [ * ] shows that o ( T ) C [ 0 , 0 ) . Q.E.D. The next lemma shows that a positive self adjoint transformation has a

Hence , by Theorem X.4.2 . , o ( T ) C ( 0 , 0 ) . Thus [ * ] shows that o ( T ) C [ 0 , 0 ) . Q.E.D. The next lemma shows that a positive self adjoint transformation has a

**unique**positive “ square root ” . 3 LEMMA .Page 1250

Finally we show that the decomposition T = PA of the theorem is

Finally we show that the decomposition T = PA of the theorem is

**unique**. ... Since A is**unique**, P is**uniquely**determined on R ( A ) by the equation of P ( Ar ) = Tx . Further the extension of P by continuity from R ( A ) to R ( A ) is ...Page 1283

Thus , equation ( e ' ) has the

Thus , equation ( e ' ) has the

**unique**solution ( cf. Lemma VII.3.4 ) and ti F = ( 1 + 0 ) -H Σ Σ ( -1 ) Φ ' Η . j = 0 1 . Since all the terms in equation ( e ) but the first are absolutely continuous , it follows that F is absolutely ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

44 other sections not shown

### Other editions - View all

### Common terms and phrases

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