## Linear Operators, Part 2 |

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Page 893

In summary we state the following theorem . 1 THEOREM . Let E be a

self adjoint spectral measure in Hilbert space defined on a field of subsets of a

set S . Then the map Í →T ( 1 ) defined by the equation 1 ( f ) = [ st ( s ) E ( ds ) , te

B ...

In summary we state the following theorem . 1 THEOREM . Let E be a

**bounded**self adjoint spectral measure in Hilbert space defined on a field of subsets of a

set S . Then the map Í →T ( 1 ) defined by the equation 1 ( f ) = [ st ( s ) E ( ds ) , te

B ...

Page 900

and thus there is a

set having E measure zero . If f is E - measurable then to is a

measurable function , i . e . , an element of the B * - algebra B ( S , E ) . The

algebra EB ...

and thus there is a

**bounded**function to on S with f ( s ) = fo ( s ) except for s in aset having E measure zero . If f is E - measurable then to is a

**bounded**E -measurable function , i . e . , an element of the B * - algebra B ( S , E ) . The

algebra EB ...

Page 1240

Semi -

extensions of those operators in a class of symmetric operators which arise

frequently from the boundary value problems of mathematical physics . 1

DEFINITION .

Semi -

**bounded**Symmetric Operators In this section we study the self adjointextensions of those operators in a class of symmetric operators which arise

frequently from the boundary value problems of mathematical physics . 1

DEFINITION .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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