## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2046

Corollary VIII . 1 . 16 thus shows that s ( t ) , o St < oo is a strongly continuous

semi - group and that As + B with domain D ( As ) is its infinitesimal generator .

We have already observed that 8 ( 5 ) is strongly analytic

now ...

Corollary VIII . 1 . 16 thus shows that s ( t ) , o St < oo is a strongly continuous

semi - group and that As + B with domain D ( As ) is its infinitesimal generator .

We have already observed that 8 ( 5 ) is strongly analytic

**for R**( 5 ) > 0 . We shallnow ...

Page 2389

Moreover , it follows similarly that at a point de $

A ( 10 ) = 0 ,

then 19 ( 0 | |

Moreover , it follows similarly that at a point de $

**R**for which el > 82 but for whichA ( 10 ) = 0 ,

**R**( A ) has a ... Finally , if 0 < li < oo and A + ( 11 ) + 0 , A - ( ^ , ) # 0 ,then 19 ( 0 | |

**R**( 1 ) | is bounded on a short transversal drawn to the real axis ...Page 2461

1 ) if and only if

same norm as elements of Cp 11 COROLLARY . An operator V belonging to the

trace class 6 , can be factored as V = AB , where A and B belong to the Hilbert ...

1 ) if and only if

**R**belongs to this same class Cp ; moreover , V**and R**have thesame norm as elements of Cp 11 COROLLARY . An operator V belonging to the

trace class 6 , can be factored as V = AB , where A and B belong to the Hilbert ...

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