## Linear Operators: Spectral theory |

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Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

self adjoint operator T and let f be a complex Borel function

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

**defines**an ... Let E be the resolution of the identity for theself adjoint operator T and let f be a complex Borel function

**defined**E - almost ...Page 1548

extensions of S and Ŝ respectively , and let 2n ( T ) and 2n ( Î ) be the numbers

space Hı , and let T , be a self adjoint operator in Hilbert space Hz .

operator ...

extensions of S and Ŝ respectively , and let 2n ( T ) and 2n ( Î ) be the numbers

**defined**for the self adjoint operators T ... be a self adjoint operator in Hilbertspace Hı , and let T , be a self adjoint operator in Hilbert space Hz .

**Define**theoperator ...

Page 1647

In connection with

identical . Thus , by Lemma 3 , a distribution F corresponds to a unique

continuous ...

In connection with

**Definition**4 , it should be noted that two continuous functions**defined**in I which differ at most on a Lebesgue null set are in fact everywhereidentical . Thus , by Lemma 3 , a distribution F corresponds to a unique

continuous ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure 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