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

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Page 893

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

adjoint spectral measure in Hilbert space defined on a field of subsets of a set S.

Then the map f T ( 1 ) defined by the equation T ( 1 ) = $$ + ( s ) E ( ds ) , fe B ( S ...

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

**bounded**selfadjoint spectral measure in Hilbert space defined on a field of subsets of a set S.

Then the map f T ( 1 ) defined by the equation T ( 1 ) = $$ + ( s ) E ( ds ) , fe B ( S ...

Page 900

and thus there is a

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

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

EB ( S ...

and thus there is a

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

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

EB ( S ...

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

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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