## Linear Operators: Spectral theory |

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Page 890

... the sum of all the projections E(A) for which 2, e3, then the function E is a

resolution of the identity for T and the operational calculus is given by the

(vi) f(t) = s.s., f(a)B(an), where the integral is defined as the finite sum X-1 f(A,) E(A

).

... the sum of all the projections E(A) for which 2, e3, then the function E is a

resolution of the identity for T and the operational calculus is given by the

**formula**(vi) f(t) = s.s., f(a)B(an), where the integral is defined as the finite sum X-1 f(A,) E(A

).

Page 1089

This

Top!” = (Tp, Top) = (T*Top, p), we see our lemma to be a special case of the “

minimax

4.8.

This

**formula**may be written (u,(T))* = min max |Two. (7,71) = ... (p, wa)=0 SinceTop!” = (Tp, Top) = (T*Top, p), we see our lemma to be a special case of the “

minimax

**formula**” for the eigenvalues of a compact operator, given as Theorem X.4.8.

Page 1363

basis for this

projection in the resolution of the identity for T corresponding to (A1, A2) may be

calculated from the resolvent by the

ie; ...

basis for this

**formula**is found in Theorem XII.2.10 which asserts that theprojection in the resolution of the identity for T corresponding to (A1, A2) may be

calculated from the resolvent by the

**formula**1 FA2-3 E((A1, A,))f = lim lim I, [R(4—ie; ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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