## Linear Operators: Spectral operators |

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Results 1-3 of 73

Page 1931

+ 4 COROLLARY . If the

- field , then E is countably additive in the strong operator topology and bounded .

The boundedness of E ( o ) follows from Corollaries IV . 10 . 2 and II . 3 . 21 .

+ 4 COROLLARY . If the

**domain**of a countably additive spectral measure E is a o- field , then E is countably additive in the strong operator topology and bounded .

The boundedness of E ( o ) follows from Corollaries IV . 10 . 2 and II . 3 . 21 .

Page 2087

68 Let As be the operator of the preceding exercise and let B be an arbitrary

bounded linear operator in Hp . Then ( i ) The operator Ag + B with

( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S (

t ) ...

68 Let As be the operator of the preceding exercise and let B be an arbitrary

bounded linear operator in Hp . Then ( i ) The operator Ag + B with

**domain**( p ) T( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S (

t ) ...

Page 2256

Q . E . D . where C is a finite collection of closed Jordan curves bounding a

being oriented in the customary positive sense of complex variable theory . The

curves C ...

Q . E . D . where C is a finite collection of closed Jordan curves bounding a

**domain**D , containing the union of o ( T ' ) and a neighborhood of infinity , C ,being oriented in the customary positive sense of complex variable theory . The

curves C ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero