## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1188

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has

been

necessarily bounded and this concept is formulated in the following

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has

been

**defined**by the identity ( Tx , y ) ... space adjoint of an operator which is notnecessarily bounded and this concept is formulated in the following

**definition**.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 | 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 | be a complex Borel function

**defined**E - almost ...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

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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