## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1955

We shall be concerned with the fine structure of the

points of an operator in X will be classified , as they were in Hilbert space ,

according to the following definition . + 1 DEFINITION . Let A be a bounded linear

...

We shall be concerned with the fine structure of the

**spectrum**, and the spectralpoints of an operator in X will be classified , as they were in Hilbert space ,

according to the following definition . + 1 DEFINITION . Let A be a bounded linear

...

Page 1957

Thus , by the preceding corollary , we have O ( S . ) Soc ( To ) , and so to prove

the present corollary , it suffices to prove that , is in the continuous

. Let ( S – XI ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same ...

Thus , by the preceding corollary , we have O ( S . ) Soc ( To ) , and so to prove

the present corollary , it suffices to prove that , is in the continuous

**spectrum**of Sg. Let ( S – XI ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same ...

Page 2507

uniformly bounded by a constant K in the neighborhood of the

while the integrals ( ( 1 + i€ ) 1 – H ) – 15 / 2 dx and + 8 8 + 8 1 + ie ) I – Hz ) - 10 |

2d ) are bounded as a →0 . In this case , and under the additional assumption

that ...

uniformly bounded by a constant K in the neighborhood of the

**spectrum**of H ,while the integrals ( ( 1 + i€ ) 1 – H ) – 15 / 2 dx and + 8 8 + 8 1 + ie ) I – Hz ) - 10 |

2d ) are bounded as a →0 . In this case , and under the additional assumption

that ...

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