## Linear Operators, Part 2 |

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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 8 , 7 , 8 ] as an element of the graph of T1 ( T) . Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( t ) ) is

complete in the

**norm**\ . Since the two additional terms in Ila are the**norm**of | as ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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