## Linear Operators: Spectral theory |

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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

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

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