## Linear Operators: Spectral theory |

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Page 893

Let E be a

field of subsets of a set S . Then the map Í → T ( 1 ) defined by the equation T ( 4 )

= 15 / ( s ) E ( ds ) , te 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 of subsets of a set S . Then the map Í → T ( 1 ) defined by the equation T ( 4 )

= 15 / ( s ) E ( ds ) , te 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 fo 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 1 ( s ) = fo ( s ) except for s in aset having E measure zero . If f is E - measurable then fo is a

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

algebra EB ...

Page 1455

( a ) If T is a closed symmetric operator in Hilbert space which is

and whose essential spectrum 04 ( T ) does not intersect the interval ( - 00 , 2 ) of

the real axis , we say that T is finite below a . ( b ) If i is a formally symmetric

formal ...

( a ) If T is a closed symmetric operator in Hilbert space which is

**bounded**belowand whose essential spectrum 04 ( T ) does not intersect the interval ( - 00 , 2 ) of

the real axis , we say that T is finite below a . ( b ) If i is a formally symmetric

formal ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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