## Linear Operators: Spectral theory |

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Page 1015

If lim T = T in the

the integral in [+] contains a(Ta) for all sufficiently large n. From Corollary VII.6.3 it

is seen that, in the

...

If lim T = T in the

**norm**of HS it follows from Lemma VII.6.5 that the contour C ofthe integral in [+] contains a(Ta) for all sufficiently large n. From Corollary VII.6.3 it

is seen that, in the

**norm**of HS+, lim [A, -T.]−1 = [A, -T]−1 rt-o-oxo uniformly for A...

Page 1297

The first

Now Ti(r) is an adjoint (Theorem 10); therefore (cf. XII.1.6) £(T(r)) is complete in

the

of ...

The first

**norm**is the**norm**of the pair [f, Tif) as an element of the graph of Ti(r).Now Ti(r) is an adjoint (Theorem 10); therefore (cf. XII.1.6) £(T(r)) is complete in

the

**norm**|f|1. Since the two additional terms in f2 are the**norm**of f as an elementof ...

Page 1699

F. is the limit in the

g,(a) = 0 for a in Ce—L, it follows from Definition 3.15 that per's is the limit in the

F. is the limit in the

**norm**of H*)(L) of a sequence {g}} of functions in Co(L). Puttingg,(a) = 0 for a in Ce—L, it follows from Definition 3.15 that per's is the limit in the

**norm**of Ho(Ce) of the sequence {g}} of elements of Co(Ce). Hence, by Lemma ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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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