## Linear Operators: Spectral theory |

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Page 1088

( s , t ) in SxS , and suppose that K ( s , t ) = K ( t , 8 ) , so that ( Kf ) ( s ) = ( K ( s , t )

/ ( t ) u ( dt ) defines a

enumeration of the eigenfunctions of K , and { u ; } an enumeration of the

corresponding ...

( s , t ) in SxS , and suppose that K ( s , t ) = K ( t , 8 ) , so that ( Kf ) ( s ) = ( K ( s , t )

/ ( t ) u ( dt ) defines a

**compact operator**in L ( S , E , u ) . Let { Pi } be anenumeration of the eigenfunctions of K , and { u ; } an enumeration of the

corresponding ...

Page 1089

These numbers are called the characteristic numbers of the operator T ; we write

un ( T ) for the nth characteristic number of T . In terms of these characteristic

numbers , we may define various norms for and classes of

These numbers are called the characteristic numbers of the operator T ; we write

un ( T ) for the nth characteristic number of T . In terms of these characteristic

numbers , we may define various norms for and classes of

**compact operators**.Page 1095

If Tn € C , is a sequence of operators such that T . - Tmbo → 0 as m , n → 00 ,

there exists a

→ 0 . Proof . By Lemma 9 ( a ) and the fact that the family of

...

If Tn € C , is a sequence of operators such that T . - Tmbo → 0 as m , n → 00 ,

there exists a

**compact operator**T such that Tn →T ( in the topology of Cp ) as n→ 0 . Proof . By Lemma 9 ( a ) and the fact that the family of

**compact operators**is...

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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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