## Linear Operators: Spectral theory |

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Page 1017

calculate the trace of A relative to the

= Σας , , = Σ α , α , = C- ' Σ α . , 95 , c - 1 § a ;, Y3 9 j = 1 and so , n CAC - lyi = £

aijYj . = j = 1 From this it follows that the trace of CAC - 1 , calculated relative to

the ...

calculate the trace of A relative to the

**basis**Yı , ... , Yn . Note that n AC - 1 yi = Αα ,= Σας , , = Σ α , α , = C- ' Σ α . , 95 , c - 1 § a ;, Y3 9 j = 1 and so , n CAC - lyi = £

aijYj . = j = 1 From this it follows that the trace of CAC - 1 , calculated relative to

the ...

Page 1028

Let { Xq , & E A } be an orthonormal

may suppose without loss of generality that there is a finite subset B of A such

that { Xq , a € B } is an orthonormal

Let { Xq , & E A } be an orthonormal

**basis**for $ . Since EH is finite dimensional wemay suppose without loss of generality that there is a finite subset B of A such

that { Xq , a € B } is an orthonormal

**basis**for EH , and { Xq , a € A - B } is an ...Page 1029

Let ' n be orthogonal to S and have norm one so that { x1 , ... , xn } is an

orthonormal

ÀI ) x ;, æ ; ) and has ( ( T - ÎI ) x ;, æ ; ) = 0 fori > i . This completes the construction

of the ...

Let ' n be orthogonal to S and have norm one so that { x1 , ... , xn } is an

orthonormal

**basis**for E " . Then the matrix of T - Îl in terms of { x1 , ... , xn } is ( ( T-ÀI ) x ;, æ ; ) and has ( ( T - ÎI ) x ;, æ ; ) = 0 fori > i . This completes the construction

of the ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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