## Linear Operators: Spectral theory |

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Page 1088

...

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

. Show that if g = Kf for some f in L2 ( S , E , y ) , then g is continuous and the

eigenfunction ...

...

**compact operator**in L ( S , £ , u ) . Let { i } be an enumeration of theeigenfunctions of K , and { u ; } an enumeration of the corresponding eigenvalues

. Show that if g = Kf for some f in L2 ( S , E , y ) , then g is continuous and the

eigenfunction ...

Page 1089

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

m ( 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

m ( 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 The C , is a sequence of operators such that Tn - Tmle 0 as m , n → 00 , there

exists a

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

closed ...

If The C , is a sequence of operators such that Tn - Tmle 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**isclosed ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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