## Linear Operators: Spectral operators |

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Page 2021

82 81 For each s in R2 this matrix is normal and ( 23 ) Â ( 8 ) Â * ( 8 ) = 18/21 = A *

( s ) Â ( s ) , SE R2 , so that * Â ( s ) ( Â ( s ) ( 24 ) = I , 08 R2 181 181

) shows that 1s | --Â ( s ) is unitary for 8 +0 . Thus post ( 4 ( 25 ) Â - ( 8 ) = WS ...

82 81 For each s in R2 this matrix is normal and ( 23 ) Â ( 8 ) Â * ( 8 ) = 18/21 = A *

( s ) Â ( s ) , SE R2 , so that * Â ( s ) ( Â ( s ) ( 24 ) = I , 08 R2 181 181

**Equation**( 24) shows that 1s | --Â ( s ) is unitary for 8 +0 . Thus post ( 4 ( 25 ) Â - ( 8 ) = WS ...

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The first

second from the fact that they belong to the commutative algebra A ,, and

operator ...

The first

**equation**in ( 27 ) follows from the definitions of the operators $ ( f + ) , thesecond from the fact that they belong to the commutative algebra A ,, and

**equation**( 28 ) follows from ( 26 ) . With each operator a in A , we associate anoperator ...

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Now let y be an arbitrary vector in H + and define the vector x by the

) . Then ( 31 ) shows that x is in H. and

some vector 2 in H- we have e619- ty = e - Be - 519 + ) 2 +2 , and , using ( 30 ) ...

Now let y be an arbitrary vector in H + and define the vector x by the

**equation**( 36) . Then ( 31 ) shows that x is in H. and

**equation**( 35 ) holds . This means that forsome vector 2 in H- we have e619- ty = e - Be - 519 + ) 2 +2 , and , using ( 30 ) ...

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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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