## Linear Operators: Spectral theory |

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Page 949

On the other hand, it has been

isomorphic with C(S), where S is a compact Abelian group, and also (Lemma 3)

that the continuous characters of S are of the form e”. By Theorem 1.6, the set of ...

On the other hand, it has been

**seen**(Theorem 2) that AP is isometric andisomorphic with C(S), where S is a compact Abelian group, and also (Lemma 3)

that the continuous characters of S are of the form e”. By Theorem 1.6, the set of ...

Page 1024

A. (i) det(I–Bw)|= (1+ ) II (1–4) N i-1 A Since (1/N) tr(B)| < 1 and A # A, the inverse

operator (I–BN)-l exists and it is readily

Therefore (I–B)+| < |(I–BN)-" and so (ii) det(I–BN)|(I–B)-"| < |det(I–Bw)|(I–BN)-"|.

A. (i) det(I–Bw)|= (1+ ) II (1–4) N i-1 A Since (1/N) tr(B)| < 1 and A # A, the inverse

operator (I–BN)-l exists and it is readily

**seen**that a-brow-sa-Bro. (i+. to)" w -Therefore (I–B)+| < |(I–BN)-" and so (ii) det(I–BN)|(I–B)-"| < |det(I–Bw)|(I–BN)-"|.

Page 1154

Since it is clear that 2%) = 2×2, what will be proved then, is that (i) 2%)(E) = c(2

x2)(E), E e X(2), for some constant c independent of E. This condition (i), as is

...

Since it is clear that 2%) = 2×2, what will be proved then, is that (i) 2%)(E) = c(2

x2)(E), E e X(2), for some constant c independent of E. This condition (i), as is

**seen**from Corollary III.11.6, is a consequence of the assertion that (ii) 2%)(A X B)...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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