## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1015

If lim Tn = T in the

the integral in [ * ] contains o ( T ) for all sufficiently large n . From Corollary VII.6.3

it is seen that , in the

If lim Tn = T in the

**norm**of HS it follows from Lemma VII.6.5 that the contour C ofthe integral in [ * ] contains o ( T ) for all sufficiently large n . From Corollary VII.6.3

it is seen that , in the

**norm**of HS + , lim [ A , TJ - = [ A , -T ]uniformly for 2 in C.Page 1297

The first

Now T ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( Ti ( t ) ) is

complete in the

as an ...

The first

**norm**is the**norm**of the pair [ 1 , T / ] as an element of the graph of T ( T ) .Now T ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( Ti ( t ) ) is

complete in the

**norm**I / 1 . Since the two additional terms in Ila are the**norm**of fas an ...

Page 1639

1 + ult ; J , m ) This

- space . If k < oo and I is compact , but not otherwise , the spaces C ' ( I ) and C ( I

) are B - spaces under a

1 + ult ; J , m ) This

**norm**makes each of the spaces listed above into a complete F- space . If k < oo and I is compact , but not otherwise , the spaces C ' ( I ) and C ( I

) are B - spaces under a

**norm**equivalent to the**norm**displayed , though not ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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