## Linear Operators: Spectral operators |

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Page 1926

If T is a normal operator , then ( T - NIE ( a ) = 0 and this formula reduces to the

formula f ( T ) = { f ( a ) E ( A ) , 1€ ( T ) which is not valid for an

more clearly the difference between the calculi given by these two formulas , let

us ...

If T is a normal operator , then ( T - NIE ( a ) = 0 and this formula reduces to the

formula f ( T ) = { f ( a ) E ( A ) , 1€ ( T ) which is not valid for an

**arbitrary**T . To seemore clearly the difference between the calculi given by these two formulas , let

us ...

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

...

under the involution A → A * , it follows that the map ( ayy ) → ( bij ) is an

involution in the algebra M ( B ( H ) ) and that , with this involution , Mp ( B ( H ) ) is

a B ...

...

**arbitrary**, shows that bun = a * v . Since B ( HP ) is a B * - algebra ( IX . 3 . 2 )under the involution A → A * , it follows that the map ( ayy ) → ( bij ) is an

involution in the algebra M ( B ( H ) ) and that , with this involution , Mp ( B ( H ) ) is

a B ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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