## Linear Operators: Spectral operators |

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Page 1926

REO ( T ) In terms of N and E the operational calculus for an

takes the form $ ( 7 ) = MOJE ( da ) , o ( 7 ) whereas if T is normal only the first

term f ( T ) = f ( ) E ( DA ) O ( T ) of this series is needed to express f ( T ) . Since ,

as ...

REO ( T ) In terms of N and E the operational calculus for an

**arbitrary**operatortakes the form $ ( 7 ) = MOJE ( da ) , o ( 7 ) whereas if T is normal only the first

term f ( T ) = f ( ) E ( DA ) O ( T ) of this series is needed to express f ( T ) . Since ,

as ...

Page 1941

By the above , this shows that o ( N ) $ C . , and since ε > 0 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 ...

By the above , this shows that o ( N ) $ C . , and since ε > 0 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 ...

Page 1963

... which , since x and y are

- algebra ( IX . 3 . 2 ) under the involution A →A * , it follows that the map ( ajj ) → (

bis ) is an involution in the algebra M , ( B ( H ) ) and that , with this involution ...

... which , since x and y are

**arbitrary**, shows that byw = arv . Since B ( H ' ) is a B *- algebra ( IX . 3 . 2 ) under the involution A →A * , it follows that the map ( ajj ) → (

bis ) is an involution in the algebra M , ( B ( H ) ) and that , with this involution ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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