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

### From inside the book

Results 1-3 of 85

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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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 Nauk 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