## Linear Operators: Spectral theory |

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Page 893

Let E be a

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

, fe B ( S , E ) , is a continuous * - homomorphic map of the B * - algebra B ( S , E )

...

Let E be a

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

, fe B ( S , E ) , is a continuous * - homomorphic map of the B * - algebra B ( S , E )

...

Page 900

and thus there is a

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 ( S ...

and thus there is a

**bounded**function to on S with f ( s ) = f ( s ) except for s in a sethaving 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 ( S ...

Page 1455

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

and whose essential spectrum ( T ) does not intersect the interval ( - 0 , 2 ) of the

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

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

**bounded**belowand whose essential spectrum ( T ) does not intersect the interval ( - 0 , 2 ) of the

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

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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