## Linear Operators: Spectral theory |

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Page 1017

calculate the trace of A relative to the

cozov, j=1 and so, CAC-1 y, -2", $/; . From this it follows that the trace of CAC-4,

calculated relative to the

proved ...

calculate the trace of A relative to the

**basis**yi, ..., ya. Note that acou, -4-, -2°,-,-cozov, j=1 and so, CAC-1 y, -2", $/; . From this it follows that the trace of CAC-4,

calculated relative to the

**basis**{yi, ..., y,}, is X-1 air. By what has already beenproved ...

Page 1029

Then, since S is necessarily invariant under T, there exists by the inductive

hypothesis, an orthonormal

a, be orthogonal to S and have norm one so that {ri, ..., a,} is an orthonormal

for ...

Then, since S is necessarily invariant under T, there exists by the inductive

hypothesis, an orthonormal

**basis**{ri,..., r, 1} for S with ((T-21)r, w,) = 0 for j > i. Leta, be orthogonal to S and have norm one so that {ri, ..., a,} is an orthonormal

**basis**for ...

Page 1344

It is readily seen, by a similar argument, that p,(A) depends continuously on A. It

then follows easily from Corollary X.7.8 that E,(A) = E(M(4); p,(A)) depends

continuously on A, i = 1,..., k. Let v1,..., v, be an orthonormal

E ...

It is readily seen, by a similar argument, that p,(A) depends continuously on A. It

then follows easily from Corollary X.7.8 that E,(A) = E(M(4); p,(A)) depends

continuously on A, i = 1,..., k. Let v1,..., v, be an orthonormal

**basis**for E" such thatE ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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