## Linear Operators: Spectral theory |

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Page 1297

The first

Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( ) ) is

complete in the

as ...

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 ( T ( ) ) is

complete in the

**norm**Iflı . Since the two additional terms in 112 are the**norm**of fas ...

Page 1431

( e ) The closure of D ( Tolt ' ) ) in the

of D ( T . ( t ' ) ) in the

( i ' ) ) in the

( e ) The closure of D ( Tolt ' ) ) in the

**norm**of D ( Tilt ' ) ) coincides with the closureof D ( T . ( t ' ) ) in the

**norm**of D ( T ( T ) ) . Let D , and Dy be the closures of D ( T .( i ' ) ) in the

**norms**of D ( T1 ( 7 ' ) ) and D ( T1 ( T ) ) respectively . By step ( c ) ...Page 1639

1 + ulf ; J , m ) This

- space . If k < oo and I is compact , but not otherwise , the spaces Cl ( 1 ) and Cr (

I ) are B - spaces under a

1 + ulf ; 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 Cl ( 1 ) and Cr (

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

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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