## Linear Operators: Spectral operators |

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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

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 .Page 2073

The first

The first

**equation**in ( 27 ) follows from the definitions of the operators $ ( f + ) , the second from the fact that they belong to the commutative algebra A ,, and**equation**( 28 ) follows from ( 26 ) .Page 2074

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

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 for some vector 2 in H- we have e619- ty = e - Be - 519 + ) 2 +2 ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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