## Linear Operators: Spectral theory |

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Page 1017

calculate the trace of A relative to the

αγα , c - 1 § ( 1995 ) j - 1 j = 1 and so , CAC " y . -2 CAC - lyi = aij y ; 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 AC - lyi = Axi Σαγα , c - 1 § ( 1995 ) j - 1 j = 1 and so , CAC " y . -2 CAC - lyi = aij y ; j = 1 From this

it follows that the trace of CAC - 1 , calculated relative to the

**basis**{ 91 , ... , yn } ...Page 1028

Let { xq , 0 € A } be an orthonormal

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

that { xa , A E B } is an orthonormal

Let { xq , 0 € A } be an orthonormal

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

that { xa , A E B } is an orthonormal

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

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

and has ( ( T - ÀI ) xi , x ; ) = 0 for ; > i . This completes the construction of the ...

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

**basis**for En . Then the matrix of T - îl in terms of { x1 , ... , xn } is ( ( T - Â1 ) x ;, x ; )and has ( ( T - ÀI ) xi , x ; ) = 0 for ; > i . This completes the construction of the ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero