## Linear Operators: Spectral theory |

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Page 893

Let E be a

field E of subsets of a set S . Then the map | →T ( f ) defined by the equation T ( f )

= | - | ( 8 ) E ( ds ) , fe B ( S , E ) , is a continuous * - homomorphic map of the B ...

Let E be a

**bounded**self adjoint spectral measure in Hilbert space defined on afield E of subsets of a set S . Then the map | →T ( f ) defined by the equation T ( f )

= | - | ( 8 ) E ( ds ) , fe B ( S , E ) , is a continuous * - homomorphic map of the 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

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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