## Linear Operators: Spectral operators |

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Page 2242

T = T ( f ) in the sense of

unbounded spectral operator of scalar type . The projection valued measure E is

said to be the resolution of the identity for T . 13 LEMMA . An unbounded spectral

...

T = T ( f ) in the sense of

**Definition**10 , where f ( z ) = 2 , then T is said to be anunbounded spectral operator of scalar type . The projection valued measure E is

said to be the resolution of the identity for T . 13 LEMMA . An unbounded spectral

...

Page 2590

6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

spectrum of , XV . 4 . 3 ( 1939 ) Quasi - nilpotent part of a spectral operator ,

XV . 4 .

6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

**definition**of , XV . 4 . 2 ( 1938 )spectrum of , XV . 4 . 3 ( 1939 ) Quasi - nilpotent part of a spectral operator ,

**definition**of , XV . 4 . 6 ( 1941 ) Radical part of a spectral operator ,**definition**of ,XV . 4 .

Page 2591

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. countably

additive , XV . 2 ( 1930 ) , XV . 2 . 3 ( 1930 ) , XV . 2 . 4 ( 1931 )

. 1 ( 1929 ) integral with respect to , XV . 2 ( 1929 ) Spectral operator , adjoint of ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. countably

additive , XV . 2 ( 1930 ) , XV . 2 . 3 ( 1930 ) , XV . 2 . 4 ( 1931 )

**definition**of , XV . 2. 1 ( 1929 ) integral with respect to , XV . 2 ( 1929 ) Spectral operator , adjoint of ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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### Common terms and phrases

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