## Linear Operators: Spectral operators |

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Page 1926

Since , as this example shows , the theory of normal operators is not an infallible

guide even to the theory of

must revert to more general considerations in attempting to construct the desired

...

Since , as this example shows , the theory of normal operators is not an infallible

guide even to the theory of

**arbitrary**operators in finite dimensional spaces , wemust revert to more general considerations in attempting to construct the desired

...

Page 1941

By the above , this shows that o ( N ) C. , and since ε > O is

that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent .

Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral

operator ...

By the above , this shows that o ( N ) C. , and since ε > O is

**arbitrary**, it followsthat o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent .

Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral

operator ...

Page 1963

... the corresponding matrix elements any belong to a commutative B * -

subalgebra of B ( H ) . The algebra AP will now be defined explicitly in terms of

the notion of a spectral measure space . Let S be an

of sets in S ...

... the corresponding matrix elements any belong to a commutative B * -

subalgebra of B ( H ) . The algebra AP will now be defined explicitly in terms of

the notion of a spectral measure space . Let S be an

**arbitrary**set and < a o - fieldof sets in S ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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