## Linear Operators, Volume 2 |

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Page 1010

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

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 ...Page 1015

If lim Tn T in the

If lim Tn 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 that , in the**norm**of HS + , lim ( 2 , -T . ) - 1 ...Page 1297

The first

The first

**norm**is the**norm**of the pair [ f , T / ] as an element of the graph of Ti ( t ) . Now Ti ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( T1 ( ) ) is complete in the**norm**\ / lı . Since the two additional ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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