## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1027

Hence a

scalar 2

have ETx = 2x . Then Tx = x + y , where y

...

Hence a

**belongs**to the spectrum of ET . Conversely , suppose that a non - zeroscalar 2

**belongs**to the spectrum of ET . Then , for some non - zero æ in EH , wehave ETx = 2x . Then Tx = x + y , where y

**belongs**to the subspace ( I - E ) H , and...

Page 1116

Then plainly | B9 : 12 < ( 7/7/2 ) 2 < 0 , so that , by Definition 6.1 , B

Hilbert - Schmidt class Cz . If we let Aqi = yi - p / 2 Pi , then A is plainly self adjoint

and A

Then plainly | B9 : 12 < ( 7/7/2 ) 2 < 0 , so that , by Definition 6.1 , B

**belongs**to theHilbert - Schmidt class Cz . If we let Aqi = yi - p / 2 Pi , then A is plainly self adjoint

and A

**belongs**to the class Cr , where r ( 1 – p / 2 ) = p , i.e. , r = p ( 1 - p / 2 ) -1 .Page 1602

Then the point 2

14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real

solution of the equation ( 1-1 ) = 0 on ( 0 , 0 ) which is not square - integrable but

...

Then the point 2

**belongs**to the essential spectrum of 7 ( Hartman and Wintner [14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let | be a real

solution of the equation ( 1-1 ) = 0 on ( 0 , 0 ) which is not square - integrable but

...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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