## Linear Operators: Spectral theory |

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Page 1010

The number | | T | | is sometimes called the Hilbert - Schmidt

. In this definition of the class HS a particular orthonormal sequence was used .

The number | | T | | is sometimes called the Hilbert - Schmidt

**norm**or the double -**norm**of T . The class of all Hilbert - Schmidt operators on H will be denoted by HS. In this definition of the class HS a particular orthonormal sequence was used .

Page 1015

By hypothesis f ( 0 ) = 0 and so f ( T ) = U and is therefore in HS . If lim T , = T in

the

[ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII . 6 . 3 it is seen ...

By hypothesis f ( 0 ) = 0 and so f ( T ) = U and is therefore in HS . If lim T , = T in

the

**norm**of HS it follows from Lemma VII . 6 . 5 that the contour C of the integral in[ * ] contains o ( Tn ) for all sufficiently large n . From Corollary VII . 6 . 3 it is seen ...

Page 1297

The first

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

complete in the

The first

**norm**is the**norm**of the pair [ f , T1 / ] as an element of the graph of T ( T ). Now T ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( T ) ) is

complete in the

**norm**\ tlı . Since the two additional terms in I / 2 are the**norm**of f ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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